The region in the -plane is bounded by the graphs of and

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

The region in the

xy

-plane is bounded by the graphs of

x = y + 2

and

x = y^{2}

. Which of the following definite integrals gives the exact area of this region? (a)

\displaystyle \int_{-1}^{2} \bigl(y^{2} - (y+2)\bigr)\,dy

(b)

\displaystyle \int_{0}^{2} \bigl((y+2) - y^{2}\bigr)\,dy

(c)

\displaystyle \int_{-1}^{2} \bigl((y+2) - y^{2}\bigr)\,dy

(d)

\displaystyle \int_{-1}^{2} (y+2)\,dy