Question

Area bounded by the parabola $y=4x^2$, y-axis and the lines y=1, y=4 is

• A. 3 sq. unit
• B. $\frac{7}{5}$ sq. unit
• C. $\frac{7}{3}$ sq. unit
• D. None of these

Answer 1

The correct option is C $\frac{7}{3}$ sq. unit

Required area = ${\int }_1^{4}xdy={\int }_1^4\frac{\sqrt{y}}{2}dy$
$=\frac{1}{2}.\frac{2}{3}{\left|y^{\frac{3}{2}}\right|}_1^4=\frac{7}{3}$ sq. unit.