Mathematics

Evaluate the following integral:$\displaystyle\int { \cfrac { 1 }{ \cos { 2x } +3\sin ^{ 2 }{ x } } } dx$

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

Realted Questions

Q1 Single Correct Hard
Solve:-
$\int\limits_0^1 {\frac{{dx}}{{{{({x^2} + 1)}^{3/2}}}}}$
• A. $1$
• B. $\sqrt 2$
• C. $\dfrac{1}{\sqrt 2}$
• D. $1/2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Resolve into partial fraction $\displaystyle \frac{x^3-3x-2}{(x^2+x+1)(x+1)^2}$
• A. $\displaystyle \frac{3x-1}{x^2+x+1}+\frac{2}{(x+1)^2}+\frac{3}{(x+1)}$
• B. $\displaystyle \frac{3x}{x^2+x+1}+\frac{2}{(x+1)^2}-\frac{3}{(x+1)}$
• C. $\displaystyle \frac{x-1}{x^2+x+1}+\frac{2}{(x+1)^2}-\frac{3}{(x+1)}$
• D. $\displaystyle \frac{3x-1}{x^2+x+1}+\frac{2}{(x+1)^2}-\frac{3}{(x+1)}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \overset{2\pi}{\underset{0}{\int}} x \,log \left(\dfrac{3 + \cos x}{3 - \cos x}\right)dx$
• A. $\dfrac{\pi}{12} \,log \,3$
• B. $\dfrac{\pi}{3} \,log \,3$
• C. $0$
• D. $\dfrac{\pi}{2} \,log \,3$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The value of I(n)=$\displaystyle \int_{0}^{\pi}\dfrac{sin^2n\theta}{sin^2\theta}d\theta$ is $(\forall n \in N)$
• A. $\dfrac{n\pi}{2}$
• B. $\dfrac{n\pi}{4}$
• C. None of these
• D. $n\pi$

Let $\displaystyle I_{1}=\int_{0}^{1}(1-x^{2})^{1/3} dx$  &  $\displaystyle I_{2}=\int_{0}^{1}(1-x^{3})^{1/2} dx$