Find the definite integral?

Question

Find ∫ 1/(sqrt(4-x^2)) dx from 1 to 2.

 

Answer: (1/3)pi

Answer 1

the integral is sin^-1(x/2) evaluated between 1 and 2 which is an angle whose sine is 1-an angle whose sine is 1/2 which is π/2-π/6=π/3

 

Regards

 

Jim

Answer 2

∫[4 - x²]^-½ dx = sin^-1 (x/2) evaluated between 1 and 2

 

sin^-1(2) - sin^-1(1/2) = (1/3)pi