The curve and the vertical line bound a finite planar region S.

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

The curve

y^{2}+2y-x=0

and the vertical line

x=2

bound a finite planar region S. (a) Express

x

explicitly as a function of

y

using the equation

y^{2}+2y-x=0

. (b) Determine the exact

y

–coordinates of all intersection points of the curve with the line

x=2

. (c) Using your results from parts (a) and (b), set up a definite integral with respect to

y

whose value equals the area of S, then evaluate the integral to obtain the exact area.