Question

I: The area bounded by the curve $y=x^3$ and the ordinates $x=-2$ and $x=1$ with X-axis is $\frac{17}{4}$sq. units.
II: The area bounded by the parabola $y^2=x$ and the straight line $y=4$ with Y-axis is $\frac{64}{3}$ sq. units.
Which of the above statement is correct?

• A. Only I
• B. Only II
• C. Both I and II
• D. Neither I nor II.

Answer 1

The correct option is C Both I and II

I: ${\int }_{-2}^1{x}^{3}dx=-{\int }_{-2}^0{x}^{3}dx+{\int }_0^1{x}^{3}dx$
$=-{\left[\frac{x^4}{4}\right]}_{-2}^0+{\left[\frac{x^4}{4}\right]}_0^1=\frac{17}{4}$
II: ${\int }_0^{16}\sqrt{x}dx={\left[\frac{x^{3/2}}{3/2}\right]}_0^{16}=\frac{64}{3}$