(1+5x+10x^2+10x^3+5x^4+x^5 )dx= (1+x)p 6 +c then p is : - Vidyadip

MCQ

$\int\big(1+5\text{x}+10\text{x}^2+10\text{x}^3+5\text{x}^4+\text{x}^5\big)\text{dx}=\frac{(1+\text{x})\text{p}}{6}+\text{c}$ then $p$ is :

A
$5$
✓
$6$
C
$7$
D
$8$

✓

Answer

Correct option: B.

$6$

Given, $\int\big(1+5\text{x}+10\text{x}^2+10\text{x}^3+5\text{x}^4+\text{x}^5\big)\text{dx}$
$\int(\text{x+1})^5\text{dx}\ [$by binomial theorem$]$
$=(\text{x+1})^5\text{dx}=\frac{(\text{x+1})6}{6}+\text{c}$
So, the value of $p = 6$

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