Mathematics

# If $\displaystyle\int^{\pi}_0\dfrac{x^2}{(1+\sin x)^2}dx=A$ then $\displaystyle\int^{\pi}_0\dfrac{2x^2\cos^2(x/2)}{(1+\sin x)^2}dx=?$

$A+\pi -\pi^2$

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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 Medium
$\displaystyle \int\dfrac{ x^{3}\ -\ x^{2}\ +\ x\ -\ 1}{x\ -\ 1}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Solve: $\displaystyle\lim_{n\rightarrow\infty} \left\{\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{2n}\right\}=$
• A. log $3$
• B. $4$
• C. $\dfrac{\pi}{2}$
• D. log $2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle\int \dfrac{d\theta}{\cos^{2}\theta(\tan 2\theta+\sec 2\theta)}=$
$\lambda \tan\theta+2\log_{e}|f(\theta)|+C$ where $C$ is a constant of integrating, then the ordered pair $(\lambda, f(\theta))$ is equal to:
• A. $(1,1-\tan\theta)$
• B. $(-1,1-\tan\theta)$
• C. $(-1,1+\tan\theta)$
• D. $(1,1+\tan\theta)$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle\int\dfrac{e^x}{x}(1+x\log |x|)\ dx=$
• A. $e^x\log|x|+e^x+c$
• B. $e^x\log|s|-x+c$
• C. none of these
• D. $e^x\log |x|+c$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$