You are here:

Calculus/Integral Question

Advertisement

Expert: - 11/24/2011


Question
Problem
Problem  
If F(x) is continuous and the integral of f(x) from 0 to 4 = 10 then compute the integral of f(2x) from 0 to 2.

Answer
S f(x) dx from 0 to 4 is 10. Make the change of variables x=2y , then dx/dy = 2 and dx = 2 dy . Since y = (1/2)x , the new limits for the integral in the variable y become 0 to 2.

We now have 10 = S f(x) dx from 0 to 4 = S f(2y)(2)dy from 0 to 2 =  2 S f(2y)dy from 0 to 2

So 10 = 2 S f(2y)dy from 0 to 2  and 5 = S f(2y)dy from 0 to 2

Since the name we give to the variable does not matter , we now have S f(2x)dx from 0 to 2 = 5

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Socrates

Expertise

I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

Experience

Ph.D. in Mathematics and many years teaching Calculus at state universities.

Education/Credentials
B.S. , M.S. , Ph.D.

©2012 About.com, a part of The New York Times Company. All rights reserved.