Chapter 6.3, Problem 3QQ

To determine

To find the value of k.

Answer to Problem 3QQ

  $k=2$ & option C is correct.

Explanation of Solution

Given:

  ${\displaystyle \underset{2}{\overset{k}{\int }}{x}^{2}dx}=0$

Calculation:

  $\begin{array}{l}{\displaystyle \underset{2}{\overset{k}{\int }}{x}^{2}dx}=0\\ \Rightarrow {\left[\frac{x^3}{3}\right]}_2^k=0\\ \Rightarrow \frac{k^3}{3}-\frac{2^3}{3}=0\\ \Rightarrow \frac{k^3}{3}=\frac{8}{3}\\ \Rightarrow k^3=8\\ \Rightarrow k=2\end{array}$

Hence option C is correct.