Mathematics

# Evaluate the following definite integral :$\displaystyle \int _{\pi /6}^{\pi /4} \ \text{cosec} \ x \ dx$

##### SOLUTION
Now,
$\displaystyle \int _{\pi /6}^{\pi /4} \ \text{cosec} \ x \ dx$

$=\left[\log|(cosec x-\cot x)|\right]_{\tfrac{\pi}{4}}^{\tfrac{\pi}{6}}$ [ Using direct formula]

$=\log|(2-\sqrt{3})|-\log|(\sqrt{2}-1)|$

$=\log\left|\dfrac{2-\sqrt3}{\sqrt2-1}\right|$

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

#### Realted Questions

Q1 Multiple Correct Medium
If $f\left( x \right)$ satisfies the relation $f\left( \dfrac { 5x-3y }{ 2 } \right) =\dfrac { 5f\left( x \right) -3f\left( y \right) }{ 2 } \forall \ x,y\in R$ and $\ f\left( 0 \right) =3$ and $f^{ ' }\left( 0 \right) =2$, then the period of $\sin { \left( f\left( x \right) \right) }$ is
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• D. $3\pi$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
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Q4 Single Correct Medium
$\displaystyle \int{\dfrac{x^{3}-1}{x^{3}+x}dx}$ equal to
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