Question

Area of the region (in square units) bounded by the curve $y=x^{2}+4$ and the line $y=5 x-2$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{12}$
• C. 2
• D. $\frac{1}{6}$

Answer 1

Answer: (D)

We have,
$y=x^{2}+4, y=5 x-2$
Solving equation, we get

$(2, 8)$ and $(3,13)$
Area of shaded region
$\int\limits_{2}^{3}\left((5 x-2)-\left(x^{2}+4\right) d x\right. $
$=\int\limits_{2}^{3}\left(5 x-x^{2}-6\right) d x=\left[\frac{5 x^{2}}{2}-\frac{x^{3}}{3}-6 x\right]_{2}^{1} $
$=\left[\left(\frac{45}{2}-9-18\right)-\left(10-\frac{8}{3}-12\right)\right]=\frac{1}{6}$