Mathematics

# If $\int \dfrac{dx}{(x-\sqrt{x^{2}-1})^{2}}= Ax^{3}+Bx^{2}+Cx+D(x^{2}-1)^{3/2}+E$, then

$A=\dfrac{2}{3}, B=0, C=-1$

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

#### Realted Questions

Q1 Subjective Medium
Integrate the function   $\displaystyle \frac {\cos x}{\sqrt {1+\sin x}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Evaluate the given integral.
$\displaystyle \int { \cfrac { { e }^{ x }\left( 1+x \right) }{ \cos ^{ 2 }{ \left( x{ e }^{ x } \right) } } } dx$
• A. $2\log _{ e }{ \cos { \left( x{ e }^{ x } \right) } } +C$
• B. $\sec { \left( x{ e }^{ x } \right) +C }$
• C. $\tan { \left( x+{ e }^{ x } \right) } +C$
• D. $\tan { \left( x{ e }^{ x } \right) } +C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the definite integral   $\displaystyle \int_2^3\frac {dx}{x^2-1}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integrals:
$\int { \sqrt { 2x-{ x }^{ 2 } } } dx\quad$

The average value of a function f(x) over the interval, [a,b] is the number $\displaystyle \mu =\frac{1}{b-a}\int_{a}^{b}f\left ( x \right )dx$
The square root $\displaystyle \left \{ \frac{1}{b-a}\int_{a}^{b}\left [ f\left ( x \right ) \right ]^{2}dx \right \}^{1/2}$ is called the root mean square of f on [a, b]. The average value of $\displaystyle \mu$ is attained id f is continuous on [a, b].