Home
Class 12
MATHS
Evaluate : int0^(2pi)e^xcos(pi/4+x/2)dx...

Evaluate : `int_0^(2pi)e^xcos(pi/4+x/2)dx`

Text Solution

Verified by Experts

Let,`( x/2​+π/4​=θ)`
` x=2θ−π/2` and `dx=2dθ`
Thus, `2int_(pi/4)^(5pi/4)e^(2theta-pi/2)cos(theta)d theta`
=`2e^(-pi/2)I_1`
Where`I_1`=`2int_(pi/4)^(5pi/4)e^(2theta)cos(theta)d theta`
=`1​/4e^(2θ)[(2cosθ+sinθ)]_(π/4)^(5π/4)-(1/4​)I_1`
or `5I_1/4=1/4[e^(5pi/2)​(-2 ...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int_0^(2pi)cos^5x\ dx

Evaluate int_0^(pi/2) xcosx dx

Evaluate: int_0^(pi/2) xcotx dx

Evaluate : int_0^(pi/2) x sinx dx

Evaluate: int_0^(pi//2) e^x (sinx-cos x) dx

Evaluate: int_0^(pi//2) e^x (sinx-cosx) dx

Evaluate int_0^(pi/2) cos^2x dx

Evaluate: int_0^(2pi)1/(1+e^(sin x))dx

Evaluate :int_(0)^( pi)e^(2x)*sin((pi)/(4)+x)dx