Question

Fundamental Theorem of Calculus to evaluate

Answer 1

\[\int\limits_{-\pi}^{\pi} f(x) dx\]
\[f(x)= 4x if -\pi \le x \le0\]
\[f(x)=3\sin(x) if 0 \le x \le \pi\]

Answer 2

i got the answer -25.7392

Answer 3

but this is not the right answer

Answer 4

Well, you have a piecewise function, so you had best divide your interval into, well, pieces :)
\[\int\limits_{-\pi}^{\pi}f(x)dx = \int\limits_{-\pi}^{0}f(x)dx+\int\limits_{0}^{\pi}f(x)dx\]
And now you can substitute f(x), but importantly, a different function for those two integrals...

Answer 5

I divided the info into two seperate integrals
one going from -pi to 0 and one going form 0 to pi

for the 1st
(4*-x^2)/2

for the 2nd
(3*cos(x))

Answer 6

Is this right?

Answer 7

never mind i got the right answer