Mathematics

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


ANSWER

$$A+\pi -\pi^2$$


View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
$$\displaystyle \int\dfrac{ x^{3}\ -\ x^{2}\ +\ x\ -\ 1}{x\ -\ 1}\ dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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 $$ 2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$(1,1+\tan\theta)$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$e^x\log |x|+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate:
$$ \int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer