Question

$\int x^{5} d x =________$

$\frac{x^{6}}{6} + k$
$\frac{x^{5}}{5} + k$
$\frac{x^{7}}{7} + k$
$\frac{x^{8}}{8} + k$

Answer: $\frac{x^{6}}{6} + k$

Solution :-

\begin{aligned} \int x^{5} d x & = & \frac{x^{5 + 1}}{5 + 1} + k (∵ \int x^{n} d x = \frac{x^{n + 1}}{n + 1} + k) \\ = & \frac{x^{6}}{6} + k \end{aligned}

So, correct answer is option-1, $\to \frac{x^{6}}{6} + k$

#Integration #BSEB PYQ 2017 #Mathematics #BSEB PYQs