Mathematics

# Evaluate the following integrals$\int { \cfrac { 1 }{ 3+4\cot { x } } } dx\quad$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle\int^{\pi/2}_{\pi/4}\dfrac{(1-3\cos x)}{\sin^2x}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate
$\displaystyle \int {x.\,\,\,{{\sin }^2}x\,\,dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\displaystyle I_{1} = \int_{0}^{\frac{\pi}2} f(\sin 2x) \sin x\>dx$
and $\displaystyle I_{2} = \int_{0}^{\frac{\pi}4} f(\cos 2x) \cos x\>dx,$ then $\displaystyle \frac{I_{1}}{I_{2}}$ is equal to
• A. $1$
• B. $\dfrac{1}{\sqrt{2}}$
• C. $2$
• D. $\sqrt{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
What is $\int { (x^2 + 1)^{\frac{5}{2}}xdx}$ equal to ?
Where c is a constant of integration.
• A. $(x^2 + 1)^{\frac{7}{2}}+c$
• B. $\frac{2}{7} (x^2 + 1)^{\frac{7}{2}}+c$
• C. None of the above.
• D. $\frac{1}{7} (x^2 + 1)^{\frac{7}{2}}+c$

Prove that $\displaystyle\int_0^{\pi/2}$ $ln(\sin x)dx=\displaystyle\int_0^{\pi/2}ln(cos x)dx=\int_0^{\pi/2}\,\,ln(sin2x)dx=-\dfrac{\pi}{2}.ln 2$.