Question

One value of $k$ which the area of thefigure bounded by the curve $y=8x^2-x^5$, the straight lines $x=1$ and $x=k$ the $x$-axis is equal to $\frac{16}{3}$, is

• A. $-1$
• B. $3$
• C. $2$
• D. $\sqrt[3]{38-\sqrt{17}}$

Answer 1

The correct option is A $-1$

${\int }_1^c(8x^2-x^5)dx=\frac{16}{3}$
$\Rightarrow {[\frac{8x^3}{3}-\frac{x^6}{6}]}_1^c=\frac{16}{3}\Rightarrow c=-1$