How do you integrate

Question

square root of (4-x^2) ?

Pleasee help!

Answer 1

put x = 2 sin(t)

then dx = 2 cos(t) dt

sqrt[4 - x^2] dx = 2 cos^2(t) dt

Then, you use:

cos^2(t) = 1/2[cos(2t) + 1]

Answer 2

Correection:

sqrt[4 - x^2] dx = 4 cos^2(t) dt