Mathematics

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


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

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Integrate:

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Evaluate: $$\displaystyle\int {\frac{1}{{{a^x}{b^x}}}} \,dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer