Homework SourseFind the area of the region in the first quadrant bounded on
Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the curve x = 2*sqrt(y), above left by the curve x = (y-1)^2, and above right by the line x = 3-y.
Solution
the curve y = 2/sqrtx y = 1 + sqrtx intersects at 2/sqrtx = 1 + sqrtx 2 = sqrtx + x 0 = x + sqrtx - 2 x = 1, plugging in x = 1 to the equation and y = 2 so point of intersection of the two curve is at (1,2) integrate from 0 to 1 1 + sqrtx - (x/4) dx the curve y = 2/sqrt(x) intersects y=x/4 2/sqrt(x) = x/4 8 = x^(3/2) x = 4 integrate from 1 to 4 (2/sqrtx) - (x/4) dx
