Mathematics

# The value of $\int \sqrt{\dfrac{1-\cos x}{\cos \alpha-\cos x}}dx$ where $0 < \alpha < x < \pi$, is equal to

$2\sqrt{2}\ \ell n\left(\cos \dfrac{\alpha}{2}-\cos \dfrac{x}{2}\right)+C$

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

#### Realted Questions

Q1 Subjective Hard
$I = \int \sqrt{\frac{a+x}{a-x}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $\displaystyle f\left ( a+b-x \right )= f\left ( x \right )$ then $\displaystyle \int_{a}^{b}xf\left ( x \right )dx$ is equal to
• A. $\displaystyle \frac{b-a}{2}\int_{a}^{b}f\left ( x \right )dx$
• B. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( a+b-x \right )dx$
• C. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( b-x \right )dx$
• D. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( x \right )dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Integrate with respect to $x$:
$\dfrac {1-\sin x}{x+\cos x}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate : $\int _{ 0 }^{ \pi /2 }{ sinxdx }$.

$\displaystyle\int \left(e^x\right)^2 e^x dx$ is equal to