AP EAMCET · Maths · Indefinite Integration
\(\int\left(\sum_{r=0}^{\infty} \frac{x^r 3^r}{r!}\right) d x=\)
- A \(e^x+c\)
- B \(\frac{e^{3 x}}{3}+c\)
- C \(3 e^{3 \mathrm{x}}+c\)
- D \(3 e^{\mathrm{x}}+c\)
Answer & Solution
Correct Answer
(B) \(\frac{e^{3 x}}{3}+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \sum_{r=0}^{\infty} \frac{x^r 3^r}{r!}=\frac{(3 x)^0}{0!}+\frac{3 x}{1!}+\frac{(3 x)^2}{2!}+\frac{(3 x)^3}{3!} \ldots . . \infty=e^{3 x} \\ & \int \sum_{r=0}^{\infty} \frac{x^r 3^r}{\lfloor r} d x=\int e^{3 x} d x=\frac{e^{3 x}}{3}+c\end{aligned}\)
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