calculus

The area enclosed between y=x^2 and y=sinx in the first quadrant can be found by calculating the integral of the lower boundary, y=x^2, from 0 to some upper limit, x=a, and subtracting the integral of the upper boundary, y=sinx, from 0 to the same upper limit, x=a. Therefore, the area is: Area = ∫0a x^2dx - ∫0a sinxdx = [x^3/3]0a - [-cosx]0a = (a^3/3)+cos(a) Note: This only applies to the first quadrant, as the upper bound of the integral only goes to x = a, which is within the first quadrant.