(a) Prove that ∫ cos^2 xdx = x/2 + sin2x/4 + C (b) Find ∫1/ √(2x - x^2)dx

Question

(a) Prove that \(\int cos^2 xdx = \frac{x}{2} + \frac{sin2x}{4} + c\)

(b) Find \(\int\frac{1}{\sqrt{2x-x^2}}\)dx

(c) Find \(\int x cos\, xdx\)

Answer 1

= sin^-1 (x-1) +c

(c) \(\int \)x cosx dx = x sinx - \(\int \)sinxdx

= x sinx + cosx + c