Q87 / 150 · MHT CET 2022 (07 Aug Shift 2) · Mathematics

$\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots . .+a^{n-1}\right) d x=$ (where $C$ is a constant of integration)

  • Correct answer
    A
    $\frac{x^{n+1}}{n+1}-a^n x+C$
  • B
    $x^n-a^n+C$
  • C
    $\frac{x^{n+1}}{n+1}-a^n+C$
  • D
    $n a^{n-1}+C$

Solution

$\begin{aligned} & \int(x-a)\left(x^{n-1}+x^{n-2} \cdot a+\ldots \ldots+a^{n-1}\right) d x \\ & =\int\left(x^n-a^n\right) d x \\ & =\frac{x^{n+1}}{n+1}-a^n x+c\end{aligned}$

Hence, the correct answer is option: 'A'.

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