ey, the preview seems to be messed up. whenever i click "preview" it doesn't change anything and i have to reload the page in order to get it to work, and when i turn off preview mode i lose a bunch of stuff i wrote.
my notebook says that we can rewrite the integral
$$\int {75\sin^3(x) \cos^2(x)dx}$$
as
$$\int {75 \cos^2(x)\sin(x)dx} - \int {75\sin(x)\cos^4(x)dx}$$
however, i have literally no idea how it got to this point, and i unfortunately can't really provide an "attempt at a solution" for this...
Ah i completely forgot about that!
I have 1 more question though, After the correction I got 2 answers ##(a= -1/sqrt3, b= 1/sqrt3)## from the left side and ##(a=-1, b=1)## from the right side, how do I check which of those is the correct answer? are both correct? in that case, when I plot the...
IMPORTANT: NO CALCULATORS
I assumed two points, (a, f(a)) and (b, f(b)) where b is greater than a. Since the tangent line is shared, I did
f'(a) = f'(b):
1) 4a^3 - 4a - 1 = 4b^3 - 4b - 1
2) 4a^3 - 4a = 4b^3 - 4b
3) 4(a^3 - a) = 4(b^3 - b)
4) a^3 - a = b^3 - b
5) a^3 - b^3 = a - b
6) (a...