Question

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

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

Answer 1

Answer: (D)

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

$(2,8)$ and $(3,13)$
Area of shaded region
$\underset{2}{\overset{3}{\int }}((5x-2)-\left(x^2+4\right)dx$
$=\underset{2}{\overset{3}{\int }}\left(5x-x^2-6\right)dx={\left[\frac{5x^2}{2}-\frac{x^3}{3}-6x\right]}_2^1$
$=\left[\left(\frac{45}{2}-9-18\right)-\left(10-\frac{8}{3}-12\right)\right]=\frac{1}{6}$