Question

Trigonometric Substitution Suppose √x = sin y.
(a) Use the ubstitution x = sin2 y, dx = 2sinycosydyx=sin2⁡y, dx = 2 sin⁡y cos⁡ydy to show ∫1/2 0√xdx/√1−x = ∫π/4 0 2 sin2 ydy
(b) Use the identity given in Exercise 49 to evaluate the definite integral without a calculator.