Home
Class 12
MATHS
Prove that: int(0)^(pi//2) (sinx)/(sinx ...

Prove that: `int_(0)^(pi//2) (sinx)/(sinx +cos x)d dx =(pi)/(4)`

Text Solution

AI Generated Solution

To prove that \[ \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{\sin x + \cos x} \, dx = \frac{\pi}{4}, \] we will follow a systematic approach using a property of definite integrals. ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7a|14 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7b|26 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

Prove that: int_0^(pi//2)(sin x)/(sinx-cosx)dx=pi/4

int_(0)^(pi/2) (sinx)/(1+cos^(2)x)dx

int_(0)^(pi//4) sinx(x) =?

Prove that : int_(0)^(pi) (x sin x)/(1+sinx) dx=pi((pi)/(2)-1)

int_0^(pi/2) (dx)/(4+sinx)

int_(0)^(pi//2) x sinx cos x dx=?

int_(0)^(pi)(x)/(1+sinx)dx .

Prove that int_(-pi//4)^(pi//4) log(sinx + cosx)\ dx = -pi/4\ log2.

int_(0)^(pi) x log sinx dx

Prove that (1+sqrt(2))/2lt int_(0)^(pi//2)(sinx)/x dx lt (pi+2sqrt(2))/4