Question

Find the area bounded by the curve y = x^2 and the straight line y = 2 + x

A. 4 1/6
B. 4 1/2
C. 5 1/6
D. 5 1/2

Answer 1

Hello,

$\int\limits^2_{-1} {(x+2-x^2)} \, dx = \left[\begin{array}{c} \dfrac{x^2}{2}+2x- \dfrac{x^3}{3}\end{array}\right] ^2 _{-1}\\ = \frac{4}{2} +4 - \frac{8}{3} -( \frac{1}{2} -2+ \frac{1}{3} )\\ = \frac{9}{2} =4+ \frac{1}{2}$

Answer B