# Thread: Definite integral with the integrand being squared?

1. ## Definite integral with the integrand being squared?

This is the last question I have for my final review.

Evaluate: (integrand b=2 a=1 2xdx)^2 - integrand b=2 a=1 (2x)^2 dx

I think I have the second half - I ended up with 6 after using u sub- but I am having trouble with the first half. Can I foil an integrand?

2. The way you've written it, the entire integral is squared. Is that what you meant? Or did you mean just the insides, the "2x", to be squared?

Thank you!

3. Nope, she has indicated the entire integrand is inside the parenthesis being squared. I was hoping it's as easy as solving and squaring the answer...

4. The "integrand" is the bit inside the integral; the "integrand" of $\int_1^2\, 2x\,dx$ is "2x". The integral of the square of the integrand would be $\int_1^2\, (2x)^2\, dx$.

You have squared the entire integral: $\left(\int_1^2\, 2x\, dx\right)^2$.

Which do you mean?

If the former, then integrate 4x^2 from 1 to 2. If the latter, integrate 2x from 1 to 2, and then square the numerical result.

5. Sorry, I meant integral. Yes, the entire integral is being squared as you have in the former. Thanks for verifying how to solve!