Limits of integration Definition and 84 Threads

Hello, I'm currently trying to get my Ti-89 Titanium to compute the following triple integral; f(x,y,z) = xy(1-z) where 0<x<1, 0<y<1, 0<z<1, and x+y+z<1 int(int(int(f(x,y,z),x,0,1-y-z),y,0,1-z),x,0,1) The problem is that I can't get my Ti89 to substitute in for the limits of...

I am just starting to do double integrals and came acorss an issue. I remembered from single integrals when we integrate from limits for say -1 to 1, we can double it and change integration limits to 0 to 1. Now, when is this the case? Basically, when can we not do this?

Homework Statement Invert the limits of integration of the following integrals: 1 ) \int_{0}^{4} dx \int_{0}^{x} f(x,y)dy \int_{0}^{2} dx \int_{0}^{\surd (4 - x^2)} f(x,y)dy \int_{0}^{1} dy \int_{y}^{2-y} f(x,y)dx These are 3 different integrals in 3 separate exercises, they're...

Hi guys, I've been doing past paper questions for an exam and I've gotten stuck with the limits of an integral. We have to evaluate \int\int\int _{\Omega} \frac{1}{(1+z)^2} dx dy dz where \Omega = \left\{ (x, y, z) : x^2 + y^2 \leq z^2 \leq 1 - x^2 - y^2, z \geq 0 \right\} using spherical...

Homework Statement A surface S is defined by z = 1-x^2-y^2 between 0≤ z ≤1 I need to calculate the flux of the vector field F = (y)i + (z)j through S.Homework Equations Cylindrical polar coordinates, Normal etcThe Attempt at a Solution By changing the variables using cylindrical polar...

Homework Statement Let S be the part of the plane z=f(x,y)=4x - 8y +5 above the region (x-1)^2 + (y-3)^2 <= 9 oriented with an upward pointing normal. Use Stoke's theorem to evaluate the surface integral for the vector field <2z, x, 1>. Homework Equations Stoke's Theorem is surface...

Need help in finding Limits of Integration! :) (Calc 3) Homework Statement Evaluate Integral: f * n dS, where "f" and "n" are vectors and "*" is DOT PRODUCT. Where, where (a) f = (x2, ey, 1), S: x + y + z = 1, x ≥ 0, y ≥ 0, z ≥ Homework Equations ummm none The...

Edit: I'm not sure if this post was deleted by an admin or if I just didn't click on the submit button. Apologies in advance if it was the former, but I reposted since I couldn't think of a reason why this post would be deleted Homework Statement f(x,y)=24xy for 0<= x<=1, 0<=y<=1, 0<=x+y<=1...

Homework Statement http://www.phys.uri.edu/~gerhard/PHY204/tsl330.pdf full solution here Homework Equations The Attempt at a Solution Here is solution of problem for positively charged rod. What will be the difference if I take negatively charged rod? Why I start integration from d...

If the limits of integration of my integral are from -Infinity to zero, can I change those limits such that they're from zero to +Infinity? If so, how? Thanks!

Find the area of the region in the plane enclosed by the cardioid r = 4+4\sin{\theta} The book explains that "Because r sweeps out the region as {\theta} goes from 0 to 2{\pi}, these are our limits of integration."

Homework Statement Use a triple integral to find the volume of the solid bounded by the graphs of the equations; z=9-x3 y=2-x2 y=0 z=0, x is equal to or bigger than 0Homework Equations The Attempt at a Solution Well finding the limits for z and y were simple, they are given, however...

Homework Statement The curves are: f(x)= x^{2/3} and g(x)=x^{3/2} Homework Equations I am assuming that: x^{2/3} = x^{3/2} is going to give me the limits of integration but I don't know how to solve for x on this equation. Could also put it this way...

Hello--- I've been working on a problem which requires the numerical evaluation of an improper integral. I would like to transform the limits of integration on [0,\infty) to the bounded region [a,b] by replacing the variable \omega with another variable. Here is the integral...

Ive seen some example of U substitution where the limits of integration are changed for example, Say we have a particle pushed along the x-axis with force=10/(1+x)^2 and we want the work required to move it 9 ft. so Work = the integral from [0,9] of 10/(1+x)^2(dx) U substitution gives...

Homework Statement Is Time Period = \int \frac{1}{v} dx ?? If yes, the under what limits of integration??

Homework Statement Evaluate \int(Acosx + Bsinx + C)/(acosx + bsinx +c) dx where the limits of integration are -π and π Homework Equations The Attempt at a Solution Hi everyone, My question is: is the function periodic (I'm guessing it is, as it's a combination of sin...

Can you always just swap the limits of integration and flip the sign of a one-dimensional integral or is there a time when you can't do this?

Homework Statement see attached Homework Equations The Attempt at a Solution

Find the double integral of: (x+y)x dxdy Where R is a quadrilateral with vertices at (-4,-1), (-2,-2) (-1,1) and (-3,2) **I have done the diagram and i know that there will be two regions R1 and R2 but i am not sure exactly how to find the limits of int. for these two regions, any...

The question is this: Consider the tetrahedron which is bounded on three sides by the coordinate planes and on fourth side by plane x+(y/2)+(z/3)=1 I think the region to integrate over should appear in R^2 as a right triangle, is this correct? Secondly i am having much trouble finding...

Homework Statement Joint pdf given as kxy for 0 < x < y < 1. Find the value of k. The Attempt at a Solution I understand the process of finding k - doing the double integral and setting it to 1. What I don't understand is the limits of integration for y. I've seen two...

Homework Statement Find the volume of the region under the graph of f(x,y) = x+y and above the region y2≤x, 0≤x≤9 The Attempt at a Solution From these equations, x will be integrated from 0-9, but I'm not sure about y. My thinking is that y will be intgrated from 0-3 because y2≤x...

Homework Statement (a)The region R enclosed by the curves y=x and y=x^2 is rotated about the x-axis. Find the volume of the resulting solid. (b)Find the volume of the solid in part (a) obtained by rotation the region about y=2. The Attempt at a Solution I solved the (a) integral...

Homework Statement A Hemispheric bowl has a radius of a and a depth of h. Find the Volume Homework Equations r= \sqrt{a^2-y^2} \pi \int{(\sqrt{a^2-y^2)^2)} The Attempt at a Solution I solved the integral using the limits h and 0 and got \frac{\pi*h(3a^2-h^2)}{3}. But...

[SOLVED] Changing limits of integration Homework Statement Given: \int_{y=0}^\pi\int_{x= y}^{\pi}\frac{sinx}{x} dxdy Change the order of integration and evaluate the double integral. Homework Equations My professor told me, "This integral cannot be expressed in terms of...

Homework Statement Given y=x^2 , bounded by the line x=1 and y=1, first quadrant. Fairly simple problem. Homework Equations Solving for integration by y first...say, \int[\intdy]dx The Attempt at a Solution I have solved this problem, integrating by x first and y first. I'm having...

[SOLVED] limits of integration Homework Statement I want to substitute x=t^2 in \int_{-\infty}^{\infty}{\exp(-t^4)} dt. What are the new limits of integration? They are both infinity aren't they? But the integral is clearly not zero? Is the problem that the substitution rule only holds for...

Homework Statement For the given region R, find intR f(x) dA. The region has the following points: (-1,1), (-1,-2) and (3,-2) Homework Equations The Attempt at a Solution I'm having problems finding the boundaries for the integral. I know that we have: -1<=x<=3 and -2<=y<=1...

Homework Statement Integralx^3sqrt(4-9x^2)dx with limits of integration at 2/3, 0 (trig subst) Homework Equations The Attempt at a Solution x=sqrt(4/9)sin theta dx=sqrt(4/9)cosine theta sqrt(4-9x^2) sqrt(4-9*4/9sin^2theta) sqrt(4-4sin^2theta) sqrt(4(1-sin^2theta)...

Stokes' Theorem - Limits of Integration - Urgent! Please give a hand :) Homework Statement Assume the vector function \vec{A} = \hat{a}_x \left( 3x^2 y^3 \right) + \hat{a}_y \left( -x^3 y^2 \right) Evaluate \int \left( \nabla \times \vec{A} \right) \cdot d\vec{s} over the triangular...

If I'm asked to find the volume of a solid that lies below the surface z = f(x,y), and above to region in the xy-plane bounded by a certain curve...and I'm only given 3 limits of integration, what do I do? For example: z = 9 - x - y Given y = 0, x = 3, y = (2x)/3 At first I thought I...

As a problem I was asked to show that phi, as defined by: \phi_n(t) = \frac{n}{\pi(1+n^2t^2)} Satisfies the property that for any f with the property to continuious at 0, then: \lim_{n\rightarrow\infty} \int_{-\infty}^{\infty} \phi_n(t)f(t)dt = f(0) But if we let f be 1/phi, we see that it...

Hi. I have a problem with a question. Basically, I have an integral that goes from x=0 to x=1, and I'm supposed to make a change of variables like this: Let x = 1 - y^2. The problem I'm having is trying to find the limits of integration after the change of variables. Since y = +/-...