Q111 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics

$\int\left(\sum_{r=0}^{\infty} \frac{x^r 3^r}{r!}\right) d x=$

  • A
    $e^x+c$
  • Correct answer
    B
    $\frac{e^{3 x}}{3}+c$
  • C
    $3 e^{3 \mathrm{x}}+c$
  • D
    $3 e^{\mathrm{x}}+c$

Solution

$\begin{aligned} & \text { } \sum_{r=0}^{\infty} \frac{x^r 3^r}{r!}=\frac{(3 x)^0}{0!}+\frac{3 x}{1!}+\frac{(3 x)^2}{2!}+\frac{(3 x)^3}{3!} \ldots . . \infty=e^{3 x} \\ & \int \sum_{r=0}^{\infty} \frac{x^r 3^r}{\lfloor r} d x=\int e^{3 x} d x=\frac{e^{3 x}}{3}+c\end{aligned}$

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

Relevant Questions