Question

The area of the region lying in the first quadrant and bounded by $y=4x^2,x=0,y=1,y=4$ is $\frac{7}{a}$ Find a.

Answer 1

$A=(\frac{1}{2},1)$ , $B=(1,4)$

Area of the shaded region

$=4\times 1-\left(\frac{1}{2}\right)-{\int }_{\frac{1}{2}}^{1}4x^{2}dx$

$=4-\frac{1}{2}-\frac{4}{3}+\frac{1}{6}$

$=4-\frac{1}{2}-\frac{7}{6}$

$=4-\frac{10}{6}$

$=\frac{14}{6}=\frac{7}{3}$