Mathematics

# Evaluate $\int \dfrac{dx}{\sqrt{1-x}}$

$\sin^{-1} \sqrt{x}$

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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 Medium
Find the value of the following integral for $a>0$$\int _{ -\pi }^{ \pi }{ \dfrac { \cos { ^{ 2 }x } }{ 1+{ a }^{ x } } dx }$
• A. $a\pi$
• B. $2\pi$
• C. $\pi$
• D. $\pi/2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The evaluation of $\displaystyle\int{\frac{px^{\displaystyle p+2q-1}-qx^{\displaystyle q-1}}{x^{\displaystyle 2p+2q}+2x^{\displaystyle p+q}+1}dx}$ is
• A. $\displaystyle-\frac{x^p}{x^{\displaystyle p+q}+1}+C$
• B. $\displaystyle\frac{x^q}{x^{\displaystyle p+q}+1}+C$
• C. $\displaystyle\frac{x^p}{x^{\displaystyle p+q}+1}+C$
• D. $\displaystyle-\frac{x^q}{x^{\displaystyle p+q}+1}+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\int { \cfrac { dx }{ \sqrt { { x }^{ 2 }-3x+2 } } } =$?
• A. $\log { \left| x+\sqrt { { x }^{ 2 }-3x+2 } \right| } +C$
• B. $\log { \left| x-\sqrt { { x }^{ 2 }-3x+2 } \right| } +C$
• C. none of these
• D. $\log { \left| \left( x-\cfrac { 3 }{ 2 } \right) +\sqrt { { x }^{ 2 }-3x+2 } \right| } +C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integrals:
$\int { \cfrac { \cos { 2x } }{ \sqrt { \sin ^{ 2 }{ 2x } +8 } } } dx$

$\int \frac{x}{x^2 + a^2} \;dx$