Please help thanks!

Question

Sketch the region in the first quadrant enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.

 

y=2cos(x) ,    y=10sin(2x) ,    x=0

Answer 1

2cosx = 20sinxcosx; cosx = 0; x = π/2; sinx = 0.1; x = sin^-10.1

Area A = ∫_sin-1_0.1^π/2(10sin2x - 2cosx)dx = (- 5cos2x - 2sinx)_sin-1_0.1^π/2 = (5 - 2) - (- 5cos(2sin^-1(0.1)) - 0.2) = 8.1