int left(sum_{r=0}^{infty} frac{x^r 2^r}{r!}r | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) We know that the Taylor series expansion for the exponential function is given by $e^u = \sum_{r=0}^{\infty} \frac{u^r}{r!}$.Substituting $u = 2x$

Vedclass · Accepted Answer

$\frac{e^{2x}}{2} + c$

Vedclass · Answer

(D) We know that the Taylor series expansion for the exponential function is given by $e^u = \sum_{r=0}^{\infty} \frac{u^r}{r!}$.Substituting $u = 2x$ into the series,we get $\sum_{r=0}^{\infty} \frac{(2x)^r}{r!} = \sum_{r=0}^{\infty} \frac{x^r 2^r}{r!} = e^{2x}$.Now,we need to evaluate the integral $\int e^{2x} dx$.Using the integration formula $\int e^{ax} dx = \frac{e^{ax}}{a} + c$,where $a = 2$,we get $\int e^{2x} dx = \frac{e^{2x}}{2} + c$.Thus,the correct option is $D$.

$\int \left(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!}\right) dx =$

Similar Questions

$\int {e^{\log (\sin x)}} \, dx = $

$\int \sqrt{1 + \sin x} \, dx = $

If $\int \frac{f(x) \, dx}{\log \sin x} = \log \log \sin x$,then $f(x) = $

$\int (1 + 2x + 3x^2 + 4x^3 + \dots) \, dx = $

If $f(x)=x$ and $g(x)=\sin x$,then $\int f(g(x)) \, dx$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module