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

Integrate the function: $\sqrt{1-4x^2}$

$\int \frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} \, dx = $

Find the following integral: $\int (\sin x + \cos x) \, dx$

Consider the following statements $(A)$ and $(B)$:
$(A) \int_a^b \frac{d}{d x}(f(x)) d x = \frac{d}{d x} \int_a^b f(x) d x$
$(B) \frac{d}{d x} \left( \int f(x) d x \right) = f(x) + C$
Which one of the following is true?

$\int {13^x} \, dx$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module