Mathematics

# $\int _{ 0 }^{ \pi /6 }{ \dfrac { \sin { x } }{ \cos ^{ 3 }{ x } } dx } =$

$1/6$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate the following definite integrals:
$\displaystyle \int _{\pi /6}^{\pi /4} cosec \ x \ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Solve $\displaystyle\int \frac{1}{\sqrt{\left [ \sin ^{3}x\sin \left ( x+a \right ) \right ]}}dx$
• A. $\displaystyle -2cosec \alpha .\sqrt{\left ( \frac{\sin \left ( x+\alpha \right )}{\sin x} \right )}.$
• B. $\displaystyle -cosec \alpha .\sqrt{\left ( \frac{\sin \left ( x+\alpha \right )}{\sin x} \right )}+C$
• C. $\displaystyle 2cosec \alpha .\sqrt{\left ( \frac{\sin \left ( x-\alpha \right )}{\sin x} \right )}.$
• D. $\displaystyle -2cosec \alpha .\sqrt{\left ( \frac{\sin \left ( x+\alpha \right )}{\sin x} \right )} +C.$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate the function  $\displaystyle \sqrt {\sin 2x}\cos 2x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The value of $\int_{0}^{1}{\dfrac{(x^{6}-x^{3})}{(2x^{3}+1)^{3}}dx}$ is equal to :
• A. $-\dfrac{1}{6}$
• B. $-\dfrac{1}{12}$
• C. $-\dfrac{1}{18}$
• D. $-\dfrac{1}{36}$

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