Question

HELP!!! Find the area bounded by the curves y = -4sin(x) and y = sin(2x) over the closed interval from 0 to pi.

1.4

2.8

3.16

1/2

none of the above

Answer 1

I don't know if you know how to do this or not, but I will post instructions anyway.

When finding the area enclosed by two curves, the equation is \[\int\limits_{a}^{b}(f(x)-g(x)) dx\]
where f(x) is the top function and g(x) is the bottom function...literally. If you graph it out, whether on a calculator or by hand, you'll be able to tell which function encloses the region from the top and which does so from the bottom.
So when you plug the equation \[\int\limits_{0}^{\pi}(\sin(2x)-(-4\sin(x))dx\]
into your calculator, you should get 8 (at least that's what I got)
So e) none of the above.