integrating (5-4sint)^1/2 between t=0 and t= 2pi. supposed to get answer 13.36, but i'm not gettin that?

Question

i'm not recieving the answer 13.36 when i do the working out. when i integrate i get [(5-4sint)^3/2]/3/2 x 1/-4cost and when i place the values 0 and 2pi i don't get the answer needed, so bit confused.

Answer 1

Yes, this problem is stone hard, because you cannot
work it with the fundamental theorem of calculus!
The function √(5-4*sin x) has no elementary
antiderivative. Its integral is an elliptic integral
of the second kind. You will have to use
numerical integration such as Simpson's rule
or expanding the function in a series to work the
problem.
Your mistake was that you used the power rule
where it's not applicable. That rule is only
good for polynomials, nothing else!

Answer 2

Either my math is really rusty, or this problem is stone hard or you made a mistake somewhere.
In any case, I can tell you where you went wrong with your solution. You wanted to use the power rule, which is absolutely the right thing to think of first, and you chose f(t) = (5 - 4sint)^1/2, which is reasonable but you know you need f'(t) = -4cost, which is right again. If this was a constant, you can do what you did, but not with a variable. This is very important to understand.
Let me know if you stated the problem right. I'm very curious:
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