Question

How did the lower and upper limits change?

Here is the original equation:
Integral of ( sin^7 theta ( 1-sin^2 theta ) cos theta ) dtheta FROM 0 to Pi/2

Let u = sin theta, du = cos theta dtheta

The equation then becomes

Integral of ( u^7 (1-u^2)^2 ) du
From 0 to 1

Now how did it change from 0 to Pi/2, to 0 to 1?

Answer 1

is very easy

Answer 2

Tell me please :D

Answer 3

\[\theta=0\implies u=\sin\theta=\sin0=0\]\[\theta=\frac\pi2\implies u=\sin\theta=\sin\frac\pi2=1\]

Answer 4

yes

Answer 5

Wow, thanks.