Mathematics

# $\displaystyle\int_{0}^{\dfrac{\pi }{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$

##### SOLUTION
$I=\int_{0}^{\frac{\pi }{2}}\frac{\sqrt{sin x}}{\sqrt{sin x}+\sqrt{cos x}}dx$ ------(1)
$I=\int_{0}^{\frac{\pi }{2}}\frac{\sqrt{cos x}}{\sqrt{sin x}+\sqrt{cos x}}dx$ ------ (2)
$2I=\int_{0}^{\frac{\pi }{2}}\frac{\sqrt{sin x}+\sqrt{cos x}}{\sqrt{sin x}+\sqrt{cos x}}dx$
$2I=\int_{0}^{\frac{\pi }{2}}1.dx$
$2I=[x]_{0}^{\frac{\pi }{2}}=\frac{\pi }{2}$
$[I=\frac{\pi }{4}]$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Evaluate the following integral:
$\displaystyle \int { \cfrac { x }{ \sqrt { 4-{ x }^{ 4 } } } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate the function  $\displaystyle \frac {\cos \sqrt x}{\sqrt x}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \frac{1}{(x+1)(x^{2}+2x+2)}=\displaystyle \frac{A}{x+1}+\displaystyle \frac{Bx+C}{(x+1)^{2}+1}\Rightarrow A+B=$
• A. 2
• B. -1
• C. 1
• D.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:-
$\int\limits_0^{\dfrac{\pi}{2}} {\log \sin xdx}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $n \space\epsilon \space N$ & the A.M., G.M., H.M. & the root mean square of $n$ numbers $2n+1, 2n+2, ...,$ up to $n^{th}$ number are $A_{n}$, $G_{n}$, $H_{n}$ and $R_{n}$ respectively.
On the basis of above information answer the following questions