Mathematics

$$\displaystyle\int^{\dfrac{\pi}{2}}_0\dfrac{\sin x}{1+\cos^2x}dx$$.


SOLUTION
Putting $$\cos x = t$$ 
$$-\sin x = dt$$
$$\displaystyle \int_0^1 \cfrac{1}{1+t^2} dt$$
$$\displaystyle \Big[\tan^{-1} t\Big]_0^1$$
$$\implies \cfrac{\pi}{4}$$ 
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
Solve $$\displaystyle  \int { { x }^{ 2 }.\sin {2 x }\ dx }$$
  • A. $$ \dfrac { { x }^{ 2 }\cos { 2x } }{ 2 } +\dfrac { 2x\sin { 2x } }{ 4 } +\dfrac { 2\cos { 2x } }{ 8 } +c$$
  • B. $$ \dfrac { -{ x }^{ 2 }\cos { 2x } }{ 2 } -\dfrac { x\sin { 2x } }{ 2 } +\dfrac { \sin{ 2x } }{ 8 } +c$$
  • C. $$None$$
  • D. $$ \dfrac { {- x }^{ 2 }\cos { 2x } }{ 2 } +\dfrac { 2x\sin { 2x } }{ 4 } +\dfrac { 2\cos { 2x } }{ 8 } +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
Evaluate: $$\displaystyle \int \dfrac{1}{x \,log \,x \,log (log \,x)}dx$$
  • A. $$log(log(x))+c$$
  • B. $$log(log(log(\dfrac{1}{x})))+c$$
  • C. $$log(log(\dfrac{1}{x}))+c$$
  • D. $$log(log(log(x)))+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
$$\int {{e^{\sqrt x }}dx} $$ is equals to.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
Integrate $$\displaystyle \int \dfrac {x}{x+10}dx$$
  • A. $$x+10\ln|x+10|+C$$
  • B. $$x+10\ln|x|+C$$
  • C. None
  • D. $$x-10\ln|x+10|+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Evaluate the following : $$\displaystyle\int \dfrac{1}{x^{2}+8x+12}.dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer