This is one of the example problems in my book to show how to deal with integrating trigonometric functions to higher powers, by breaking them down into identities.
$$=\int cos^5x dx$$
$$=\int (cos^2x)^2cos^x dx $$
$$=\int (1-sin^2x)^2*d(sin x)$$
$$=\int (1-u^2)^2 du$$
$$=\int 1-2u^2 + u^4...
Oh, okay. I know how to do that. The trick is anti-deriving with a variable in the exponent. For example, if I expand it and then split it into three integrands and try tackle each one by itself, I trip up on the first one: $$ e^{2y} $$.
The best I can come up with is:
$$ \frac{1}{2 \ln{2}...
Hi @MarkFL,
Thanks for the response. When you say expand the integrand, do you mean like this?
S = $$\frac{1}{2}\pi \int e^{2y} + 2 + e^{-2y}$$
If so, how do I use the Fundamental Theorem of Calculus. I know what FTOC stands for but I never learned it as a thing by itself. I was taught how to...
Here's the problem I was given:
Find the area of the surface generated by revolving the curve
$$x=\frac{e^y + e^{-y} }{2}$$
from 0 $$\leq$$ y $$\leq$$ ln(2) about the y-axis.
I tried the normal route first...
g(y) = x = $$\frac{1}{2} (e^y + e^{-y})$$
g'(y) = dx/dy = $$\frac{1}{2} (e^y -...