Mathematics

# The value of $\displaystyle \int { \dfrac { dx }{ \sqrt { { x-x }^{ 2 } } } :\left( x>\dfrac { 1 }{ 2 } \right) }$ is equal to

$\sin^{-1}(2x-1)+C$

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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
$\displaystyle \int\frac{e^{x}}{(2e^{x}-3)^{2}}dx=$
• A. $\displaystyle \frac{1}{2e^{x}-3}+c$
• B. $\displaystyle \frac{1}{2(2e^{x}-3)^{2}}+c$
• C. $\displaystyle \frac{1}{(2e^{x}-3)^{2}}+c$
• D. $\displaystyle \frac{-1}{2(2e^{x}-3)}+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate: $\displaystyle \int_{\frac{\pi}{2}}^{\pi}\frac{1-sinx}{1-cosx}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int{\dfrac{(x^{2}-1)dx}{(x^{2}+1)\sqrt{x^{4}+1}}}$ is equal to :
• A. $\sec^{-1}\left(\dfrac{x^{2}+1}{\sqrt{2x}}\right)+c$
• B. $\dfrac{1}{\sqrt{2}}\sec^{-1}\left(\dfrac{x^{2}+1}{\sqrt{2x}}\right)+c$
• C. $\dfrac{1}{\sqrt{2}}\sec^{-1}\left(\dfrac{x^{2}+1}{\sqrt{2}}\right)+c$
• D. $None\ of\ these$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following : $\displaystyle\int \dfrac{1}{x^{2}+8x+12}.dx$

Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$