Mathematics

# The value of the integral $I=\int^{\infty}_{1}\dfrac {(x^{2}-2)}{x^{3}\sqrt {(x^{2}-1)}}dx$ is

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

#### Realted Questions

Q1 Single Correct Hard
Let $\displaystyle f\left ( x \right )=min\left \{ x,1-x \right \}$ for all $x \epsilon R$. Then the value of $\displaystyle \int_{0}^{2}f\left ( x \right )dx$ is
• A. $\displaystyle \frac{1}{4}$
• B. $2$
• C. $0$
• D. $\displaystyle -\frac{1}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
Solve $\displaystyle \int_{0}^{\pi /2}\frac{\cos x-\sin x}{1+\sin x\cos x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of $\displaystyle\int { \cfrac { \cos { \sqrt { x } } }{ \sqrt { x } } } dx$ is
• A. $2\cos { \sqrt { x } } +C$
• B. $\sqrt { \cfrac { \cos { x } }{ x } } +C$
• C. $\sin { \sqrt { x } } +C$
• D. $2\sin { \sqrt { x } } +C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Calculate the following integral:
$\displaystyle\, \int_{0}^{\pi }\, \frac{dx}{\cos^2\, \dfrac{x}{5}}$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$