Verify my answer for integration

[hank]

I have the following
S [ 0 to 1] (x^3 - 2x^2) - (2x^2 - 3x) dx + S [1 to 3] (2x^2 - 3x) - (x^3 - 2x^2) dx

The answer I get is 37/12.

Can someone just verify if my answer is correct?

 

[mark07]

It is correct.

Here's a useful link... "Integrator" powered by Mathematica:

http://integrals.wolfram.com/

This free web version doesn't do definite integrals but it still comes in handy when you just want to check your answers.

 

[soroban]

Hello, Hank!

\(\displaystyle \L\int^1_0\left[(x^3\,-\,2x^2)\,-\,(2x^2\,-\,3x)\right] dx\:+\:\int^3_1\left[(2x^2\,-\,3x)\,-\,(x^3\,-\,2x^2)\right]\,dx\)

The answer I get is: \(\displaystyle \L\frac{37}{12}\;\;\) . . . Me too!

You're finding the area between \(\displaystyle \,y\:=\:x^3\,-\,2x^2\,\) and \(\displaystyle \,y\:=\:2x^2\,-\,3x\;\) . . . right?