Definite integrals Definition and 79 Threads

Homework Statement F(x) = \int^{x}_{0}f(t)dt Then F'(x) = f(x) what is f'(x)? is this equivalent to f(t)? Thanks for your help M

1. Using Fourier Transforms to solve Definite Integrals with Limits 0 to Infinity I'm trying to understand how to use Fourier Transforms to solve Definite Integrals with limits from 0 to Infinity. I understand how to use Fourier Transforms to solve indefinite integrals, but I believe there...

Hi all, just wondering if someone could explain to me about define integrals. Say i have F(x)=0.5x2-2 and F(x)=x3+x2-6x and i want to find the area of the regions which is satisfied from -2 to 2. so \int0.5x2-2 from -2 to 2. \intx3+x2-6x from -2 to 2. Now with the cubic, from -2 to 0 is...

(this is not homework) Suppose I wanted to solve: \int log(x) log(x+1) dx from 0 to 1. I would turn ln(x+1) into a series, namely, –∑(-1)^n * x^n / n Any ideas? Besides substituting, pulling out the n's, and using intgration by parts?

Homework Statement Let \int_{-4}^{2} f(x) dx =9, \int_{-4}^{-2} f(x) dx=2, \int_{0}^{2} f(x)dx =3 Find (I have solved this one) \int_{-2}^{0} f(x)dx= 4 Find \int_{0}^{-2} (9 f(x)- 2)dx= ? Homework Equations \int_{a}^{b} f(x) dx = F(b) - F(a) The Attempt at a Solution I...

Homework Statement Find the average value of the function f(t) = (t-3)^2 on [0,6] Homework Equations Average value equation (see below) The Attempt at a Solution Okay, I have this: http://img4.imageshack.us/img4/5338/howthecrap.png But I don't know how it gets to the last...

Homework Statement Suppose f(x) is continuous and decreasing on the closed interval 5 <= x < 13, that f(5) = 9, f(13) = 5 and that the integral of f(x) from 5 to 13 is 70.64758. Then the integral of f^-1(x) from 5 to 9 is equal to what? (Note: f^-1(x) is the inverse of f(x))...

Homework Statement I'm trying to evaluate the problem below but the Mathematica gives me is in terms of x. Can someone please help me solve this thing. Homework Equations Integrate[((2*A)(E^(-d*((m*x^2)/h) ) ) )^2,x,{x,0,Infinity} ] The Attempt at a Solution The solution...

Homework Statement I'm not sure if I'm doing this right or not: If F(x)=\int_0^x{\sqrt{t^3+1}dt}, then find F'(2) The Attempt at a Solution \int_0^x1/2(t3+1)-1/2*3t2 1/2(x3+1)-1/2*3x2 1/2(23+1)-1/2*3(2)2 Answer=2

this is not a homework ques, but a general question.. Homework Statement if there are two functions ... f(x) and g(x) , then what does f(x)|g(x) mean. that's it. Homework Equations The Attempt at a Solution

Homework Statement The curve is rotated about the y axis, find the area of the resulting surface. y=(1/4)X2-.5ln|x| 1<_X<_2 Homework Equations S=2(pi)(f(x))\sqrt{}1+f'(x)^2 The Attempt at a Solution Alright I'm not entirely sure where to even begin. Since I'm rotating about the Y-axis I know...

Homework Statement 1)Evaluate the definite integral using FTC: \int_1^4 \left( \frac{d}{dt} \sqrt{4+3t^4} \right)dt 2)Evaluate the definite integral: \int_{-2}^6 f(x)dx f(x)= {x if x<1} {1/x if x>=1} Homework Equations The Attempt at a Solution Having trouble...

I'm taking a calculus-based physics course, and we were solving a simple differential equation for a model of drag by separating variables: (where A is some arbitrary constant) m \frac {dv} {dt} = -A v^2 - \frac {m} {A} \frac {dv} {v^2} = dt My teacher then integrates both sides, but unlike in...

Calculator program gives incorrect results (Definite Integrals/ Area)? I've inserted this definite integral into my calculator program: \int_{-1}^{2}x(x^2-4)dx and my calculator gives me -9/4 for the integral, which is what my book's answer key has written down. However, the area that...

I'm confused here.. My definite integral doesn't match by Riemman Sum... and it should right? I think that I have not integrated correctly. Can someone help me spot the problem? Thanks. Find the Area of the region bounded by: f(x)=5-x^2 , [-2, 1] Using the Riemma Sum idea (limit of the...

Homework Statement \int|x^{2}+x-2|dx from -2 to 2 Homework Equations The integral of f(x) from a to b = F(b) - F(a) |x| = { x if x >= 0; -x if x < 0 --- Ok, I don't know how to do the definite integrals of absolute values.. was never shown an example of it in class, but I kind of...

[SOLVED] Definite Integrals Homework Statement \int_{1}^{3}x^{2}dx Homework Equations The Attempt at a Solution Why is the answer 26/3? I got 4 by using the limit/Riemann Sum definition. Is this one method to calculate definite integrals?

Homework Statement Evaluate the definite integrals. Homework Equations Integral of (t+1)/(t^2+2t+1) dt from 1 to 4 (a=1, b=4) and Integral of (xe^(x^2+1)) dx from 0 to 2 (a=0, b=2) The Attempt at a Solution I have done them out, just wondering if this is the best way to...

THE AREA OF A SQUARE WITH SIDE LENGTHS EQUAL TO THE DEFINITE INTEGRAL OF (0.43890022*X) FROM 1 TO 10 please help me... Merven

ok so what has happened is my friends website is moving to a new location, he said the only way i can get to see it early is if i get the answer to this, he did this because he knows i know nothing about math... so I am one of you guys or gals can help me... THE AREA OF A SQUARE WITH SIDE...

1.5 to -1.5 6e^(3x) end up with 2e^4.5 - 2e^-4.5 (Found indefinite integral and sub'd 1.5 with x etc) The answer according to the textbook is 180.0342 - .0222 I am lost from this part. I don't know how 2e^4.5=180.0342 =180.01

Hello everyone, i have been teaching myself some basic calculus from a coupld textbooks (high-school level) my mom brought home. I'm currently in an Analysis class, next year i will be taking a BC Calc. course. My question is this, (it comes from the fact that I've kind of been skipping...

ok, my question involves two different sets of directions .. 1. Use integration to find the area of each shaded region. 2. Evaluate each definite integral. Ok, my question is this... do i do the same thing for both of these directions? .. Even further... say I have a function that...

I don't know how to solve this really easy integral. suppose: a=2 m/s^2 a = dv / dt \int^b_a a \ dt = \int^b_a dv \int^b_a 2 \ dt = v_{b} - v_{a} 2t_{b} - 2t_{a} = v_{b} - v_{a} v_{b} = v_{a} + 2t_{b} - 2t_{a} I hope everything is ok up to this point. Then I...

does anyone know how to solve definite integrals using a Ti-83 plus? my teacher said it's okay to use it to check your answer during a test, so if you know how, please let me know. also, is it possible to do indefinite integrals using ti-83 plus calculator?

I was wondering how to approximate definite integrals to within a specific accuracy. For example, how would I go about approximating the integral from 0 to 1 of sin(x^3) dx to within an accuracy of 0.001? I think I'm supposed to use the remainder estimate for the integral test, but I'm confused...

can anyone help me with this problem... the integral from 0 to half pi: 1/(1+cosx)dx... Thanks...

In the first part of the question, I proved that \int_{1/2}^{2} \frac{ln x}{1+x^2} dx = 0 Then I needed to evaluate the following but I didn't know how to do it. Can you give me some clues? I know it must be related to the definite integral that I proved in the first part, but how...

I'm now teaching myself several topics on definite integrals for a math test on monday. Here are a few problems that I don't know how to do. Q1) Prove the following inequality: 1 < [inte]pi/20 (sin x)/x dx < (pi/2) Q2) Show that for x > 0, ex-1 <= [inte]x0 (e2t+1)1/2 dt <= 21/2(ex-1)...