If f^{prime}(x)=x-frac{5}{x^5} and f(1)=4,the | vedclass

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

Question

(C) Given $f^{\prime}(x)=x-\frac{5}{x^5}$.Integrating both sides with respect to $x$,we get:$f(x) = \int \left(x - 5x^{-5}\right) dx$$f(x) = \frac{x^2

Vedclass · Accepted Answer

$\frac{x^2}{2}+\frac{5}{4} \frac{1}{x^4}+\frac{9}{4}$

Vedclass · Answer

(C) Given $f^{\prime}(x)=x-\frac{5}{x^5}$.Integrating both sides with respect to $x$,we get:$f(x) = \int \left(x - 5x^{-5}\right) dx$$f(x) = \frac{x^2}{2} - 5 \left( \frac{x^{-4}}{-4} \right) + c$$f(x) = \frac{x^2}{2} + \frac{5}{4x^4} + c$Given $f(1) = 4$,substitute $x=1$:$4 = \frac{1^2}{2} + \frac{5}{4(1)^4} + c$$4 = \frac{1}{2} + \frac{5}{4} + c$$4 = \frac{2+5}{4} + c$$4 = \frac{7}{4} + c$$c = 4 - \frac{7}{4} = \frac{16-7}{4} = \frac{9}{4}$Thus,$f(x) = \frac{x^2}{2} + \frac{5}{4x^4} + \frac{9}{4}$.

If $f^{\prime}(x)=x-\frac{5}{x^5}$ and $f(1)=4$,then $f(x)$ is

Similar Questions

If $\int \frac{x}{x \tan x+1} \, dx = \log f(x) + k$,then $f\left(\frac{\pi}{4}\right) =$

$\int \frac{dx}{a^2 - x^2}$ is equal to

The value of $\int {\frac{1}{{{{(x - 5)}^2}}}\,dx} $ is

$\int (\tan^7 x + \tan x) dx =$

$\int \frac{\sin 2x}{\sin 5x \sin 3x} \, dx = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module