Mathematics

# Solve $\dfrac{1}{2}\int{\dfrac{(-4+2x)}{\sqrt{5-4x+x^{2}}}}$

##### SOLUTION
$\dfrac{1}{2}\int{\dfrac{(-4+2x)}{\sqrt{5-4x+x^{2}}}}dx$

Let,  $5-4x+x^2=t$

$\implies(-4+2x)dx=dt$

$\implies\dfrac{1}{2}\int{\dfrac{dt}{\sqrt{t}}}$

$\implies \dfrac{2\sqrt t}{2}+C$

$\implies \sqrt{5-4x+x^2}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int \frac{1}{x\log x\log \left ( \log x \right )}dx.$
• A. $\displaystyle \left [ \log \left ( \log x \right ) \right ].$
• B. $\displaystyle \log \left [ \log \left ( \log x^{2} \right ) \right ].$
• C. $\displaystyle -\log \left [ \log \left ( \log x \right ) \right ].$
• D. $\displaystyle \log \left [ \log \left ( \log x \right ) \right ].$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle\int{\frac{dx}{(x^2+1)(x^2+4)}}=k\tan^{-1}{x}+l\tan^{-1}{\frac{x}{2}}+C$, then
• A. $\displaystyle k=\frac{1}{3}$
• B. $\displaystyle l=\frac{2}{3}$
• C. $\displaystyle l=-\frac{1}{6}$
• D. $\displaystyle k=-\frac{1}{3}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\int \frac { \cos x + 2 \sin x } { 7 \sin x - 5 \cos x } d x = a x + b \ln | 7 \sin x - 5 \cos x | + c$ then $a+b$ is
• A. $\frac { 1 } { 17 }$
• B. $\frac { 3 } { 37 }$
• C. $\frac { 23 } { 47 }$
• D. $\frac { 13 } { 37 }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Multiple Correct Hard
Let $f(x)$ be a function satisfying $f^\prime(x)=f(x)$ with $f(0)=1$ and $g$ be the function satisfying $f(x)+g(x)=x^2$. The value of the integral $\displaystyle\int_0^1{f(x)g(x)dx}$ is
• A. $e + \dfrac{{{e^2}}}{2} - \dfrac{3}{2}$
• B. $e - \dfrac{{{e^2}}}{2} - \dfrac{3}{2}$
• C. $e - \dfrac{{{e^2}}}{2} - \dfrac{5}{2}$
• D. $e + \frac{{{e^2}}}{2}$

Let g(x) =$\displaystyle \int_{0}^{x}f\left ( t \right )dt,$ where f is a function