Mathematics

# Solve : $\int {{{\sin }^{ - 1}}\left( {\cos x} \right)dx}$

##### SOLUTION
$\begin{array}{l} \int { { { \sin }^{ -1 } }\left( { \cos x } \right) dx } \\ =\int { { { \sin }^{ -1 } }\left\{ { \sin \left( { \frac { \pi }{ 2 } -x } \right) } \right\} dx } \\ =\int { \left( { \frac { \pi }{ 2 } -x } \right) dx } \\ =\frac { \pi }{ 2 } .\int { dx } -\int { xdx } \\ =\frac { { \pi x } }{ 2 } -\frac { { { x^{ 2 } } } }{ 2 } +C \end{array}$

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

#### Realted Questions

Q1 Subjective Medium
Solve :
$\displaystyle \int_{0}^{1} \cfrac{d x}{\sqrt{1+x}-\sqrt{x}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve: $\displaystyle \int \dfrac{x^3}{x - 2}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\dfrac{dy}{dx}=\dfrac{1}{x}+3x^2$ then $y=$
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• B. $\ln {x} +3x^3+c$
• C. $\ln{x} +\dfrac{x^3}{3}+c$
• D. $\ln{x} +x^3+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int\limits_{ - 1}^1 {{e^x}dx} =$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
The value of $\int_{0}^{2}\dfrac{dx}{(17+8x-4x^2)(e^{6(1-x)}+1)}$ is equal to
• A. $-\dfrac{1}{8\sqrt{21}}\log \left | \dfrac{2-\sqrt{21}}{2+\sqrt{21}} \right |$
• B. $-\dfrac{1}{8\sqrt{21}}\log \left | \dfrac{2+\sqrt{21}}{\sqrt{21}-2} \right |$
• C. $-\dfrac{1}{8\sqrt{21}}\left \{ \log \left | \dfrac{2-\sqrt{21}}{2+\sqrt{21}}\right |-\log \left | \dfrac{2+\sqrt{21}}{\sqrt{21}-2} \right | \right \}$
• D. None of these