Evaluate the definite integralsint0^(pi...

Evaluate the definite integrals`int_0^(pi/2)(cos^2x dx)/(cos^2x+4sin^2x)`

Text Solution

AI Generated Solution

To evaluate the definite integral \[ I = \int_0^{\frac{\pi}{2}} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx, \] we will follow these steps: ...

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

INTEGRALS
NCERT ENGLISH|Exercise EXERCISE 7.3|24 Videos
INTEGRALS
NCERT ENGLISH|Exercise SOLVED EXAMPLES|46 Videos
INTEGRALS
NCERT ENGLISH|Exercise EXERCISE 7.5|23 Videos
DIFFERENTIAL EQUATIONS
NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
NCERT ENGLISH|Exercise Solved Examples|13 Videos

Similar Questions

Explore conceptually related problems

Evaluate the definite integrals int_0^(pi/2)cos^2xdx

Evaluate the definite integrals int_0^(pi/2) cos2xdx

int_(0)^(pi/2) (cos^(2)x dx)/(cos^(2)x+4 sin^(2)x)

Evaluate the definite integrals int_0^(pi/4 ) (sinxcosx)/(cos^4x+sin^4x)dx

Evaluate the following integral: int_0^(pi//2)(cos^2x)dx

Evaluate the definite integrals int_0^(pi)(sin^2(x/2)-cos^2(x/2))dx

Evaluate the definite integrals int0pi/4(2sec^2x+x^3+2)dx

Evaluate the definite integrals int_0^pi(sin^2(x/2)-cos^2(x/2))dx

Evaluate the following definite integral int_0^(pi/2) cos^4 x dx

Evaluate the following definite integral int_0^(pi/2) cos^4 x dx

NCERT ENGLISH-INTEGRALS-MISCELLANEOUS EXERCISE

Evaluate the definite integralsint0^1 (dx)/(sqrt(1+x)-sqrt(x))
03:47
|
Evaluate the definite integralsint(pi/6)^(pi/3)(sinx+cosx)/(sqrt(sin2...
05:16
|
Evaluate the definite integralsint0^(pi/2)(cos^2x dx)/(cos^2x+4sin^2x...
07:57
|
Evaluate the definite integralsint0^(pi/4 ) (sinxcosx)/(cos^4x+sin^4x)...
08:15
|
Evaluate the definite integralsint(pi/2)^pie^x((1-sinx)/(1-cosx))dx
07:28
|
(sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(4))
04:06
|
Integrate the functionstan^(-1)sqrt((1-x)/(1+x))
06:47
|
Integrate the functions(x^2+x+1)/((x+1)^2(x+2)
06:51
|
Integrate the functions(2+sin2x)/(1+cos2x)e^x
03:26
|
Integrate the functionssqrt((1-sqrt(x))/(1+sqrt(x)))
05:25
|
Evaluate the definite integralsint0^(pi/4)(sinx+cosx)/(9+16sin2x)dx
09:04
|
Evaluate the definite integralsint0^(pi/2)sin2xtan^(-1)(sinx)dx
07:13
|
Choose the correct answersint(cos2x)/((sinx+cosx)^2)dxis equal(A) (-1)...
03:50
|
Evaluate the definite integralsint0^pi (xtanx)/(secx+tanx)dx
06:03
|
Evaluate the definite integralsint1^4[|x-1|+|x-2|+|x-3|]dx
08:17
|
Prove thatint1^3(dx)/(x^2(x+1))=2/3+log2/3
06:42
|
Prove thatint0^1x e^x dx=1
03:29
|
Prove thatint0^(pi/4) 2tan^3xdx=1-log2
06:59
|
Prove thatint0^(pi/2)sin^3xdx=2/3
04:36
|
Integrate the functions(sinx)/(sin(x-a)
03:32
|