Area of the region bounded by the curve $y = \left\{ \begin{array}{r} x^{2},\ x

Question

Area of the region bounded by the curve $y = \left\{ \begin{array}{r} x^{2},\ x < 0 \ x,\ \ x \geq 0 \end{array} ight.\$ and the line $y = 4$ is

Dr. Abubacker · Accepted Answer

(c)
Required area $= \int_{- 2}^{0}{\left( 4 - x^{2} \right)dx + \int_{0}^{4}{(4 - x)dx}}$
[image:8_image9.jpeg]
$= \left\lbrack 4x - \frac{x^{3}}{3} \right\rbrack_{- 2}^{0} + \left\lbrack 4x - \frac{x^{2}}{2} \right\rbrack_{0}^{4}$
$= 8 - \frac{8}{3} + 8 = \frac{40}{3}\ sq\ unit$

Q. Area of the region bounded by the curve $y = \left\{ \begin{array}{r} x^{2},\ x < 0 \\ x,\ \ x \geq 0 \end{array} \right.\$ and the line $y = 4$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?