Please help me solve the following integral. (click to see)

Question

babyslapmafro · Answer

$$\int\limits_{0}^{\pi/2}3\sqrt{\cos^4tsin^2t+\sin^4tcos^2t} dt$$

anonymous · Answer

first factor the expression within the sqrt

anonymous · Answer

$=\int_0^{\pi/2}3\sqrt{cos^2tsin^2t(cos^2t+sin^2t)}dt=\int_0^{\pi/2}3\sqrt{cos^2tsin^2t}dt=\int_0^{\pi/2}3costsintdt$
now make variable change: sint=x, cost dt = dx to get
$\int_0^{\pi/2}3x dx$

anonymous · Answer

forgot to change limits of integration: x goes from 0 to 1

anonymous · Answer

so it should be :$\int_0^13xdx$

turingtest · Answer

what is the problem that you are having @Babyslapmafro ?

noelgreco · Answer

Myko,

Your limits of integration should both be zero.

Another way is to use a trig identity:

$$\sin t \cos t=\frac{ 1 }{ 2 }\cos 2t$$