Mathematics

# Evaluate the following integrals$\int { \cfrac { 1 }{ p+q\tan { x } } } dx\quad$

##### SOLUTION

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
Let $f\left( x \right) =\frac { \sin { x } }{ x }$, then $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ f\left( x \right) f\left( \frac { \pi }{ 2 } -x \right) } dx=$
• A. $\int _{ 0 }^{ \pi }{ f\left( x \right) dx }$
• B. $\pi \int _{ 0 }^{ \pi }{ f\left( x \right) dx }$
• C. $\frac { { 1 } }{ \pi } \int _{ 0 }^{ \pi }{ f\left( x \right) dx }$
• D. $\frac { { 2 } }{ \pi } \int _{ 0 }^{ \pi }{ f\left( x \right)dx }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate the following w.r.t.$\displaystyle \int x^2\left(1-\dfrac{2}{x}\right)^2dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Assertion & Reason Hard
##### ASSERTION

$\displaystyle \int_{-1}^{1}\frac{\sin x-x^{4}}{4-\left | x \right |}dx$ is same as $\displaystyle \int_{0}^{1}\frac{-2x^{4}}{4-\left | x \right |}dx$

##### REASON

$\displaystyle \int_{-1}^{1}\left ( f\left ( x \right )+g\left ( x \right ) \right )dx=2\displaystyle \int_{0}^{1}f\left ( x \right )dx$ if $g(x)$ is an odd function and $f(x)$ is an even function.

• A. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• B. Assertion is correct but Reason is incorrect
• C. Both Assertion and Reason are incorrect
• D. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
Evaluate the integral, $\int _{ 0 }^{ 1 }{ \cos { \left( 2\cot ^{ -1 }{ \sqrt { \dfrac { 1-x }{ 1+x } } } \right) } } dx=$
• A. $1/2$
• B. $0$
• C. $1$
• D. $-1/2$

$\displaystyle \int_{1}^{4}(x^2-x)dx$