Home
Class 12
MATHS
Using properties of definite integrals, ...

Using properties of definite integrals, show that
`int_(0)^(pi//2)(sin^(2)x)/(sinx+cosx)dx=1/(sqrt(2)) log (sqrt(2)+1)`

Text Solution

Verified by Experts

The correct Answer is:
`5/6log|x-2|-5/2log|x+2|5/3log||x+1|+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (SECTION XII MOST IMPORTANT QUESTIONS FOR PRACTICE)|17 Videos

  • DIFFERENTIAL EQUATIONS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE|50 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE (MCQ)|48 Videos

Similar Questions

Explore conceptually related problems

Using properties of definite integrals, show that int_(0)^(pi//2)(xdx)/(sinx+cosx)=(pi)/(2sqrt(2))log(sqrt(2)+1)

Using property of define integrals, prove that : int_(0)^(pi//2)sin2xlogtanx dx=0

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

Using property of define integrals, prove that : int_(0)^(1) log(1/x-1)dx=0

Using property of define integrals, prove that : int_(0)^(pi//2)logcos x dx=(-pi)/2log2

Using properties of definite integral prove that int_0^2 xsqrt(2-x)dx= (16sqrt2)/15

By using the properties of definite integrals, evaluate the integral: int_0^(pi/2) (sinx-cosx)/(1+sinxcosx)dx

By using the properties of definite integrals, evaluate the integral: int_(-pi/2)^(pi/2) (sin^2x)dx

By using the properties of definite integrals, evaluate the integral: int_0^(pi/2) cos^2x dx