Definite integral Definition and 391 Threads

Consider the Integral: a=0 b=1 (x^2)(sqrt(9x+8))dx Does u=(9x+8) ? can we factor out the x^2? We have to give the value that the definite integral is

Homework Statement \int_0^a {x\sqrt{x^2+a^2}\,dx} Also, (A>0) The Attempt at a Solution Firstly, I set u=x^2+a^2 Then take the derivative, du=2x dx 1/2\int_0^a {\sqrt{u}\,du} Now I integrated. So (1/3) * [(x^2+a^2)^3/2] from a to 0. I ended up with...

Homework Statement Integrate \int_{0}^{1}\sqrt{\frac{4x^2-4x+1}{x^2-x+3}}dxHomework EquationsThe Attempt at a Solution U sub: let u=x^2-x+3 Then du=2x-1 and then have to evaluate \int_{3}^{3}\sqrt{\frac{du^2}{u}}dx But how with these limits of integration should this be 0? Not sure how to...

[SOLVED] Definite Integral of Exponential Function Homework Statement I have an integral that I need to solve for a quantum physics problem \int^{\infty}_{-\infty}e^{-a|x| - ikx}dx How would I go about solving this thing?

Definite Integral [help] ! hello, can anyone help me how to complete the following definite integral? Thanks! ∫ (x^2)*sqrt(7 x + 9) dx (From 0 to 1)

Homework Statement definite integrals (1 + 3x) dx from (-1,5) The Attempt at a Solution i keep getting 6+54 but it should be 6+36 i think i might be using the wrong property or multiplying wrong: 3[(6/n)i](6/n)

Homework Statement Find F'(x) if F(x)=\int_{0}^{x^3}(\sin (t^2))dt The Attempt at a Solution Here's what I did: F(x)= -\cos (t^2)\biggr]^{x^3}_{0} and I get: F(x)= -\cos (x^6) +1 F'(x)= sin (x^6)(6x^5) However, the book's answer is F'(x)= 3x^2 \sin(x^6) How did...

Okay, so I went a little ahead in my text and I am having alittle trouble deciphering something. To make it easy, I will provide an example/question. If I see the following problem: \int_2^42xdx, does it mean a.) Evaluate the line y=2x between 2 and 4 to get area=4. or b.)...

Show that \int_0^1 {x^n \sin \left( {\frac{{\pi x}}{2}} \right)} {\kern 1pt} dx > 0 for all {\rm{n}} \ge {\rm{0}} Basically, what i want to show is that over the interval (0,1), the integrand is above the x-axis, or positive. I will show that over the interval, both functions, x^n and...

I don't know if this question should be posted here, but I'll give it a shot anyways. I am trying to find f(x,y), which can be obtain by doing the backward Fourier integral to F(\omega_x, \omega_y). I have 2 questions. 1. Is there any Fortran code that could evaluate the (numerical)...

a=0, b= pie/3 sin theta/ cos^2 theta i let u= cos theta du/dx= -sin theta -du = sin theta sin theta/u^2 theta then i anti differentiated it -cos theta/ (1/3)(cos)^3 theta this is where i got stuck

Homework Statement The following sum \sqrt{9 - \left(\frac{3}{n}\right)^2} \cdot \frac{3}{n} + \sqrt{9 - \left(\frac{6}{n}\right)^2} \cdot \frac{3}{n} + \ldots + \sqrt{9 - \left(\frac{3 n}{n}\right)^2} \cdot \frac{3}{n} is a right Riemann sum for the definite integral. Solve as n->infinity...

Homework Statement if the integral from 0 to 4 of f(x) = -1 then what is the integral from -2 to 0 of x[f(x^2)]? Homework Equations n/a The Attempt at a Solution my first instinct is that this is an even/odd definition of an integral problem. the x squared in the function...

Homework Statement By appealing to geometric evidence show that \int_0^8x^n\,dx + \int_0^1 x^{1/n}\,dx = 1 for n a positive integer. Homework Equations Fundamental theorem of calculus, power rule for integration. The Attempt at a Solution I integrated. For the first integral, I...

Hello, Okay so I was given a density function: f(x) = 2e^(-0.25x) The problem asks for the value of Pr(X < or = 3) I first figured out the probability density function first by let \int (3,0) k.25e^(-.25x) = 1 And figured out that k = .45 and continue solving my...

Im studing for a math competition. One of the probles is as follows fnInt( (Ln(x+1)/(x^2 +1)),x,0,1) If you don't know that notation. it means Integral from 0 to 1 of Ln(x+1)/(x^2 +1) OBVIOUSLY NO CALCULATORS... I am looking for a solution, not an answer Thanks ~rosie

hi, I've been having difficulty with this integral for some time now and any help would be gratly appreciated. \int\frac{x^2 \sin x}{1+x^6}dx this is a definite integral from -pi/2 to pi/2 The sinx has been giving me problems because if I set u = to any part of the equation I can't...

i start to study integrals, i couldn't understand some things. definite integrals i didnt understand, ill show it on some eg. on v as derivative of disaonce s. the eg. was to calc how many distance s = ? does a particle travell when we throw it in air (up) and v reaches 0. so in time t = 0...

the definite integral: from a = (-pi/2) to (pi/2) f(((x^2)(sinx))/(1+x^6))dx this is the way it seems most logic to me to set it up using substitution: u = x du = dx from a = (-pi/2) to (pi/2) f(((u^2)(sinu))/(1+u^6))du = (((-cos(u))(1/3u^3))/(u+1/7u^7))+CI know how to evaluate it from...

Well as I am practising for my coming test, I encountered this question: Integrate f(x) = absolute [(sin X)^3 * (cos X)^15]dx within the interval of [0,2pi] I tried simplifying this integral into... f(x) = absolute[ ((cos X)^15)*(sin X) -((cos X)^17)*(sin X))] dx within the...

Hi, I am having trouble visualizing this problem, if anyone can help me see it, I know how to do the integral part. A church steeple is 30 feet tall with square cross sections. The square at the base has side 3 feet, the square at the top has side 6 inches, and the sides varies linearly in...

I would really like to post the work I did, but it is gibberish ! I don't know how to tackle this integral : definite integral from 0 to 1 of : ln(x)ln(1-x)dx The "traditionnal" methods don't work but I assure you that I have tried much more ! Please help

Hi, So this might be overwhelmingly stupid... But the fundamental theorem of calculus states: \int_{a}^{b}f(x)dx=F(b)-F(a) Where F is any antiderivative of f. So I have this very simple integral that I'm trying to solve...: 2\pi\int_{0}^{2}x^3\sqrt{1+9x^4}dx\rightarrow \ u=1+9x^4...

i know that this integral would take pages upon pages to solve so i m askin anyone out to there to plug it into their maple or mathlab (since mathematica doesn't return any answer) and just post the answer... i really need it \int_{\lambda=100}^{\lambda=1000} \frac{1}{\lambda^5...

Can anyone help me integrating the folowwing integrand from zero to infinity: x*ln^2(ax)*exp(-bx^2+cx) where a,b and c are real and pisitive constants. Thanks

In the Fundamental Theorem of Calculus, it is stated that lim max deltax_k -> 0 sigma f(x_k*)*deltax_k = L, where L is the definite integral of f(x) on [a,b]. How do you apply this limit definition to a normal function to find the definite integral? (Could someone give me math examples...

Hi I have a few questions regarding the following two part problem. a) Let a > 0. Use polar coordinates to evaluate \int\limits_{ - \infty }^\infty {e^{ - ax^2 + bx} } dx Ans:e^{\frac{{b^2 }}{{4a}}} \sqrt {\frac{\pi }{a}} b) Let \mathop x\limits^ \to = \left( {x_1 ,...,x_n }...

What is the integral of 110*1.10^(t) from b=35 to a=0 (b being hte upper number to the integral sign and a being the lower number to the integral sign) From the textbook it says it's the constant c=110 times the sum of the integral of b - the integral of a. so how do i get integral of a...

I am trying to evaluate this integral, \[ \int_{ - r}^r {\left( {s\sqrt {1 + \frac{{x^2 }}{{r^2 - x^2 }}} } \right)} {\rm }dx\] Is it a valid integral? If I evaluate it by plugging in r and -r, it becomes undefined. How else can I evaluate this integral? I'm in calculus 1 and I am...

hi guys yeh, I am still going through revision, and I am also stuck on this question. *integral sign*(upper limit 4, lower limit 2) x/sqrt(3x^2 + 4).dx When i look at this, i think of letting u = 3x^2 + 4, then bringing that sqrt to the top,solving for dx, and then find the integral, and...

I've been trying to determine how certain definite integrals are expressed in terms of Gamma functions. Mathematica returns the following: \int_0^1 \frac{dx}{\sqrt{1-x^4}}=\frac{\sqrt{\pi}\Gamma[\frac{5}{4}]}{\Gamma[\frac{3}{4}]} (Mapple returns a different but equivalent expression in...

There are several situations I don't know how to solve: integral of (lnx)/(x^2) dx integral of e^x(cos2x)dx integral of ln(1+x^2)dx I have a quiz tommorow, and after looking through some notes, this is what I couldn't understand. Please help! thanks.

Hello... I got a simple looking integral to solve but unfortunately couldn't do it I = \int_{0}^{1}\frac{x^2lnx}{\sqrt{1-x^2}}dx Any suggestions? Thanks and cheers Vivek

If I want to evaluate: \int^1_0 \frac {dx}{(x+1)^2} I need to use the Fundamental Theorem of Calculus right? SO wouldn't I have to solve \int^b_a \frac{dx}{(x+1)^2} = \frac{(x+1)^3}{3} = \frac {8}{3} - \frac {1}{3} ? But the answer is \frac {1}{2}

Hi I need help doing the following integration: \int_{x=0}^{x=n}[{x-\frac{1}{\sqrt{2}}]-[{x-\frac{1}{\sqrt{3}}]dx where n is an integer and [.] denotes the greatest integer function (floor), i.e. [x] = greatest integer less than or equal to x. The answer given in the book is...

Who can solve or give hint for the following integral? \int_0^4 3x \sqrt{5^2-x^2}dx :-p :eek:

I think I got pretty close to the answer to this problem. However, I just can't obtain the right approximation at the end. Please, help me find where I made a mistake. Thanks. -------------------------------------------------------------- Use a power series to approximate the definite...

Please help me! I got stuck on this problem: (1) A ball is dropped from rest, and after t seconds its velocity is v ft/sec. Neglecting air resistance, show that the average velocity during the first T/2 seconds is 1/3 of the average velocity during the next T/2 seconds. Will I integrate v? If...

ive been trying to do this problem and its annoying! The function to be integrated: 1 + 1/x + x dx Interval: [8,2] when anti differentiating the fuction i get x + x^2/2 + lnx but i don't...

Hello all, new poster here. When learning about the definition of the definite integral, a few books that I have read through first define anitdifferentiation, then explains some Riemann sums and then POOF \int_{a}^{b} f(x) dx = \lim_{||\Delta||\rightarrow\0}\sum_{i=1}^n f(\xi_i) \Delta_i x...

Hi, Physics books gloss over math. Sometimes it bothers me. Given a separable function of time and position f = h(x)g(t) then d / dt of [inte] h(x)g(t)dx = [inte] h(x) dg(t)/dt dx Where the derivative in the second integral is a partial deriv. Why the chain rule does not apply...