Mathematics

Integrate:$\displaystyle \int _{ 0 }^{ \pi /2 }{ \cos ^{ 2 }{ x } dx }$

SOLUTION
$\displaystyle \int_{0}^{\pi /2}cos^{2}x\, dx= \int_{0}^{\pi /2}cos^{2}(\frac{\pi }{2}-x)dx=I$
$\displaystyle \therefore I+I= \int_{0}^{\pi /2}cos^{2}xdx+\int_{0}^{\pi /2}sin^{2}xdx$
$\displaystyle \therefore 2I= \int_{0}^{\pi /2}1dx$
$\displaystyle \therefore 2I= \frac{\pi }{2}$
$\displaystyle \therefore I=\frac{\pi }{4}$

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
Solve: $\displaystyle \int \dfrac{\log^x}{x^3}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate :  $\int \frac { \sec x d x } { \log ( \sec x + \tan x ) }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate:

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

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Solve
$I=\displaystyle \int{\dfrac{1}{\sqrt{21+4x-4x^{2}}}dx}$

Evaluate: $\displaystyle\int {\frac{1}{{{a^x}{b^x}}}} \,dx$