Question

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

Answer 1

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

Answer 2

first factor the expression within the sqrt

Answer 3

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

Answer 4

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

Answer 5

so it should be :\(\int_0^13xdx\)

Answer 6

what is the problem that you are having @Babyslapmafro ?

Answer 7

Myko,

Your limits of integration should both be zero.

Another way is to use a trig identity:

\[\sin t \cos t=\frac{ 1 }{ 2 }\cos 2t\]