Question

How do I solve this integration Q with u substitution? Halp

Answer 1

cant be done, need to use geometric substitution. You also might be able to see that the formula of a circle, y²+x²=r² written in function of y is equal to, y = sqrt(r²-x²).

With this information you can see that you're trying to find the area of a half circle with radius 8.

Answer 2

You can use trig substitution, **x²=64sin²(φ)** i.e. **x = 8sin(φ)**

Answer 3

This is a direct form. Integral √a²-x²= x/2√a²-x² + a²/2 sininverse(x/a)

Or you can substitute x=8sintheta and solve normaly

Answer 4

Have you tried anything yet? I would start by setting u equal to everything under the radical.

Answer 5

You could always split it into 2 integrals, one from -8 to 0 and the second from 0 to 8 and then use U substitution to solve