Double integral Definition and 574 Threads

Picture of the problem is listed above. I'm not sure how to switch the bounds of integration on it. Anyone here know how to go about this? i tried doing it x^2 to 1 for y and then 0 to 1 for x but it didnt work out to be the write answer, the write answer after putting it in your calculator...

Homework Statement Evaluate the double integral \int \int_{R} ln(xy) dA where R is the rectangle bounded by x=e, x=e^2,y=1,y=e. Homework Equations ln (xy) = ln x + ln y The Attempt at a Solution I was just wondering, do I need to do anything other than take the integral with respect to x...

Homework Statement \int \int_R (x+y) dA R is the region y = x^2 and y = x^(1/2) Homework Equations I've sketched the graph and the functions are equal at (0,0) and (1,1) The Attempt at a Solution Would the limits of the integral be: \int_{0}^{1) \int_{0}^{1} (x+y) dydx...

Homework Statement Find the volume of the solid T enclosed above by the sphere x^2+ y^2 + z^2 = 2 and below by the parabloid x^2 + y^2 = z Homework Equations The double integral. Possiblly polar coordinates (x = r*cos(theta) y = r*sin(theta)). z = f(x,y) The Attempt at a Solution...

Homework Statement convert line one to polar integral and then evaluate see problems 16 attachement Homework Equations r^2=y^2+x^2 The Attempt at a Solution I changed to polar and evaluated the double integral but I come up with an answer of negative pi which seems odd since it...

Homework Statement ∫∫xy(x^2+y^2)^(1/2)dydx over the range 0 to 1 for both x and y. Homework Equations I believe that it requires integration by parts. Any help would be greatly appreciated.

Homework Statement Evaluate by changing to polar coordinates Homework Equations Can't figure out how to make the integral stop after the sqrt(9-x^2) \int_0^\frac{3}{\sqrt(2)} \int_x^{\sqrt(9-x^2)} e^-(x^2+y^2) dy dx The Attempt at a Solution I'm not sure where to really start on this one...

Homework Statement Sketch the region of integration and then evaluate the double integral: Homework Equations \int\intx2exydA over the region R= {(x,y), y<=x<=1, 0<=y<=1} The Attempt at a Solution I have managed to do half of the problem and integrate it respect to x but then...

Hi all, I am faced with this question. I am asked to show that 2(\sqrt{5}-2)\pi\leq\iint_{R}\frac{1}{\sqrt{4+sin^2x+sin^2y}}dA\leq\frac{\pi}{2} Noting that the double integral is to be performed on region R which is bounded by the circle x^2+y^2=1 From what I know, the double...

Homework Statement \int^x_0\int^y_x e^{-v} dv du where u and v are just "dummy variables" Homework Equations The Attempt at a Solution \int^x_0\int^y_x e^{-v} dv du = \int^x_0 -e^{-y} + e^{-x} du = (-e^{-y} + e^{-x})x have I made a mistake somewhere?

Hi I need to use a double integral to find the area of the region bounded by: r = 3 + 3sinQ where Q = theta. I know the bounds of the inner integral are from 0 to 3 + 3sinQ. However, I do not know how to determine the bounds of the outer integral. Any help would be greatly appreciated.

Consider the tetrahedron which is bounded on three sides by the coordinate planes and on the fourth by the plane x+(y/2)+(z/3)=1 Now the question asks to find the area of the tetrahedron which is neither vertical nor horizontal using integral calculus (a double integral)? I think they mean...

Homework Statement evaluate the integral \int\int(x^4-y^4)e^{xy}dA where R is the region bounded by xy=1, xy=2, x2-y2=1, and x2-y2=4 Homework Equations The Attempt at a Solution This is my first time on the forum, so forgive me if there are mistakes in this post. I am...

Homework Statement Evaluate the following double integral by changing the order of integration: ∫(lower 0 and upper 1)∫ (lower √x and upper 1) sin(((y^3)+1)/2) dydx [b]2. Homework Equations In case it's not clear from above! y is between √x and 1, and x is between 0 and 1. The...

Homework Statement Let f(x,y)= 1 if x is rational, 2*y if x is irrational Compute both double integrals of f(x,y) over [0,1]x[0,1] Homework Equations The Attempt at a Solution I'm tempted to say that we can do the dydx integral since when x is rational, integrating y gives...

I've written all the questions in the PDF file ... Please help me !

Homework Statement \int^{0}_{-3}\int^{\sqrt{9 - x^2}}_{- \sqrt{9 - x^2}} \sqrt{1 + x^2 + y^2} dy dx Homework Equations x = rcos(theta) y = rsin(theta) The Attempt at a Solution By making \sqrt{9 - x^2} = y then changing it to polar coordinates, I got r to be +/-3 but I'm...

Homework Statement Find the volume of the solid in the first octant by the planes z = x + y + 1 and z = 5 - x - y Homework Equations The Attempt at a Solution How would I set this up?

Homework Statement A lamina occupies the region inside the circle x^2 + y^2 = 2y but outside the circle x^2 + y^2 = 1. Find the center of mass if the density at any point is inversely proportional to its distance from the origin. Homework Equations Xcm = double integral of y*f(x,y)...

Homework Statement Consider the volume of a solid bounded by the cone: z = sqrt(x^2 + y^2) and the top half of the sphere x^2 + y^2 + z^2 = 18 that is for z >= 0 Using cylindrical coordinates, express the volume as a double integral. Homework Equations easy to sketch.. we can...

Homework Statement ok change the region R = { (x,y) | 1 <= X^2 + y^2 <= 4 , 0 <= y <= x } to polar region and perform the double integral over region R of z=arctan(y/x)dA Homework Equations r^2 = x^2 + y^2, x = r*sin(@), y = r * cos (@) The Attempt at a Solution i got R = {...

Homework Statement a) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can modelthe probability of failure of these bulbs by an exponential density function \mu = 1000, find the probability that both of the lamps bulbs will fail within 100 hours. b)...

Hi, I was just wondering if the set up for this problem; integrate f(s,t)=e^slnt over the region in the first quadrant of the st-plane that lies above the curve s=lnt from t=1 to t=2 is: integral(t=1 to t=2)integral(s=ln1 to s=ln2) of e^slnt If that's not the right set up what am I...

simple question, for "find the area of the region between the xy-plane between the curves y=x3 and x=y2 where 0<x<1 , 0<y<1 is this the double integral for x3*y2 dy dx or for the double ingeral between x3+y2 dy dx?? i assume the first one? clarification needed please, can do the rest of the...

Homework Statement Basically I'm just trying to convert a double integral into polar coordinates, but when I do it I get confused with my bounds. Homework Equations The Attempt at a Solution 4\int_0^{\infty}\int_0^{\infty}e^{-(u^2+v^2)}u^{2x-1}v^{2y-1}dudv (x and y are just numbers, not...

Homework Statement The equation is \int^{t}_{0}e^{-t'\gamma}\int^{t}_{0}e^{t''\gamma}f(t'')dt''dt'. f(t) is a random function with no known anti-derivative. I need to simplify this into a single integral of one variable. Homework Equations above. The Attempt at a Solution I moved the...

Homework Statement I have to solve the integral of (ytan^-1(x) - 3) inside the area of the rectangle with vertices (1,0), (0,1), (2,3), (3,2). How do I set up these limits? Homework Equations This is a tilted rectangle so I can't use just values for the limits? The Attempt at a...

Hi, I have a question about using the dirac function in a double integral. Lets say you have the double integral over the two values x1 and x2: int( int( sin(x1) * dirac(x1-x2) * sin(x2) )) Does this just simplify to a single integral: int( (sin(x1))^2 ) thanks!

Homework Statement Evaluate an iterated integral by reversing the order of integration \int^1_0\int^1_{y^2} ysin(x^2)dxdy Homework Equations The Attempt at a Solution I've got that the limits for x is between y^2 and 1, while the limits for y is between 0 and 1. Then I graphed...

Homework Statement Find the volume of the solid enclosed by the cylinders z=x^2, y=x^2, and the planes z=0 and y=4. Homework Equations The Attempt at a Solution ∫∫ x^2 dA For the limits of integration, I obtained y=x^2 and y=4, x=0 and x=2 I changed the order of...

Homework Statement Given the integral: \int_1^2\int_{\frac{3}{\sqrt{x}}}^{\sqrt{3}x}{{(x^2+y^2)}^{\frac{3}{2}}}dy \; dx. Convert to polar and evaluate. Homework Equations r=\sqrt{(x^2+y^2)} The Attempt at a Solution Ok, I've gotten bounds on \theta, \frac{\pi}{6} \le \theta \le...

Homework Statement \int\int_B 1 dx dy where B is the region enclosed by x^2 + y^2 = 9? What if B is the region eclosed by y = x +3, y = 5 - x, and y=8 Homework Equations The Attempt at a Solution So for x^2 + y^2 = 9, does it mean that both x and y go from -3 to 3? bot...

Homework Statement Evaluate the following integral: \int \int_R x^3 y^4 dx dy Homework Equations The Attempt at a Solution I don't even know where to start. My professor just introduced us to double integrals, now there's a strike going on at my school, so classes are...

How do you solve the double integral of xe^(xy)? bounded by x=0, y=1, x^2-y=0. I used both x-simple and y-simple methods but neither worked..I don't know what the limits are...thanks!

can someone please give me some help on this integral. it should be solvable analytically. \int^{1}_{-1}\int^{2\pi}_{0}\frac{1}{2+x+\sqrt{1-x^2}cos(y)+\sqrt{1-x^2}sin(y)}dxdy

Homework Statement How do you solve the double integral of cos(u/v) dudv, if the limits of u are v and -v, and the limits of v are 1 and 2? I tried doing it by parts but I didn't get it...

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is...

Homework Statement \int\int x^2 dA where the area D is boundd by the ellipse 5x^2 + 4xy + y^2 = 1. Homework Equations The Attempt at a Solution I'm not sure where to start this question. A few ideas I'm exploring are: 1. rewrite in polar co-ordinates (not sure how to write an...

Homework Statement \int\int e^(^x^2^+^y^2^) dA where D is the region bounded by y = sqrt(1-x^2) and y = |x|. Homework Equations The Attempt at a Solution Obviously I can draw this region out and see what it looks like, and I will have to split the integral into two for negative...

Homework Statement Apply Green's Theorem to evaluate this integral: Integral of: (6y + x) dx + (y + 2x) dy over the curve C, where C is: The circle (x - 2)^2 + (y - 3)^2 = 4 Homework Equations The Attempt at a Solution To use Green's Theorem for this I would need to figure...

This is not for a specific problem, just in general: If we want to find the double integral of a function of two varaible, when we got other 1 varaible function to define the domain. What are the basics of drawing the domain in 2d (x, y only)?

Homework Statement Given the integral shown (in attachment), make a sketch of the region of integration, express the integral with the order of integration reversed and evaluate the integral after reversing the order of integration Homework Equations The Attempt at a Solution So...

Homework Statement Given the integral (shown in attachment) make a clear sketch of the region of integration and express the integral with the order of integration reversed. Evaluate the integral you found in (ii). Homework Equations The Attempt at a Solution Everything is in...

Homework Statement Use the transformation u = 3x + 2y and v = x + 4y to evaluate: The double integral of (3x^2 + 14xy + 8y^2) dx dy for the region R in the first quadrant bounded by the lines y = -(3/2)x + 1, y = -(3/2)x + 3, y = -(1/4)x, and y = (-1/4)x + 1. Homework Equations...

Consider the double integral \int_{-\infty}^{\infty}dx f(x) \, \int_{-\infty}^{\infty}dy g(y) The first one gives 0 the second one gives infinity (diverges). Then how to express the result of the integral? Is it 0 or infinity or neither (indeterminate)? Any other comments about the integration?

Homework Statement Consider the integral shown in the sketch. Sketch the region of integration and express the integral with the reverse order of integration and evaluate it leaving your answer in surd form Homework Equations The Attempt at a Solution I shaded the area of integration but I...

Homework Statement \int_a^b\,dx\int_a^x\,dy should give area of a triangle, I can’t see how. The Attempt at a Solution \int_a^b\,dx\,{(x-a)} but then I won’t get 1/2 (ab)… (don't get the first brackets in latex between the two x)

Flux = Int B dA Why isn't this written as a double integral when we antidifferentiate over an areal?

Evaluate \int\ \int_R\ x^2e^ydA Over the rectangle R with vertices (0,0), (1,0), (1,3) and (0,3). My answer: \int\ \int_R\ x^2e^ydA = \int_0^3\ \int_0^1\ x^2e^ydA = \int_0^3\ [x^3/3]_0^1 e^y dy = 1/3 \int_0^3\ e^ydy = 1/3 (e^3-1) Double integrals are new to me, so if...

here is the problem I couldn't solve, anyone got any idea please help me. thank you very much in advance 1) use double integrals to derive the given formula for the volume of a right circular cone of radius R and height H. the volume of a cone is given by the formula (pi*R^2*H)/3 I...