Find area bounded by the curves

Question

Find the area of the region bounded by the curves , y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative.

Answer 1

hi

you need to know ∫sin^-1 ax dx = x sin ^-1ax + 1/a √1-a^2x^2

area = ∫ sin^-1 (x/4) dx = x sin^-1 (x/4) + 4 √1-(x/4)² from x = 0 to x = 4

area = 4 sin^-1 (4/4) + √1-(4/4)^2 - 0 -4 √1 - 0

area = 4 (Π/2 ) + 0 - 0 - 4

area = 2Π - 4

I hope it is useful,

Minoo