Question

Calculus help

Answer 1

\[\LARGE If~ f(x)= \int\limits \cos^4xdx+\frac{1}{3}\cot^3x-cotx \] and f(pi/2)=pi/2 then find f(x)

Answer 2

Attempt:
\[\LARGE f(x)=\frac{1}{32}(12x+8\sin2x+\sin4x)+\frac{1}{3}\cot^3x-cotx\]
\[\LARGE f(\frac{\pi}{2})=\frac{1}{32}(12 \frac{\pi}{2}-8)= \frac{\pi}{2}\]
umm now what does this mean

Answer 3

ok the trick is how to find integral of cos^4 x dx ... u have the function so find the value of it for the interval 0 to pi/2 them find f(x)

Answer 4

http://www.wolframalpha.com/input/?i=integrate+cos%28x%29%5E4

Answer 5

f(x) is what you wrote plus a constant C. You find C so that f(pi/2)=pi/2

Answer 6

i see,silly mistake! thanks!