Which definite integral represents the exact area of the region bounded by the line

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

Problem

x = 3y + 2

, the parabola

x = y^{2}

, and the horizontal lines

y = 0

and

y = 3

? (a)

\displaystyle \int_{0}^{3} \bigl(y^{2}-(3y+2)\bigr)\,dy

(b)

\displaystyle \int_{0}^{3} (3y + 2 - y^{2})\,dy

(c)

\displaystyle \int_{0}^{3} (3y + 2 - y^{2})\,dx

(d)

\displaystyle \int_{2}^{11} (3y + 2 - y^{2})\,dy