Home
Class 12
MATHS
By using the properties of definte, prov...

By using the properties of definte, prove that
`int_(0)^(pi//2)(sin^(3)x)/(sin^(3)x+cos^(3)x)dx=(pi)/4`

Text Solution

Verified by Experts

The correct Answer is:
`pi/4`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    ACCURATE PUBLICATION|Exercise QUESTION CARRYING 1 MARK - TYPE-I|36 Videos
  • DEFINITE INTEGRALS

    ACCURATE PUBLICATION|Exercise QUESTION CARRYING 1 MARK - TYPE-II|21 Videos
  • CONTINUITY

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 4 MARKS|17 Videos
  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise (Question carrying 6 marks)|7 Videos

Similar Questions

Explore conceptually related problems

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(sinx)/(sinx+cosx)=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)cos^(2)x dx=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+tan^(3)x)dx=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+sqrt(cotx))=(pi)/4

By using the properties of definte, prove that int_(0)^(pi)(e^(cosx))/(e^(cosx)+e^(-cosx))dx=(pi)/2

By using the properties of definte, prove that int_(0)^(pi//2)(sqrt(cotx))/(sqrt(tanx)+sqrt(cotx))=(pi)/4

Evaluate int_(0)^(pi//2)(cos^(5)x)/(sin^(5)x+cos^(5)x)dx

By using the properties of definte, prove that int_(0)^(a)1/(x+sqrt(a^(2)-x^(2)))=(pi)/4