Home
Class 12
MATHS
If m and n are positive integers and m n...

If m and n are positive integers and `m ne n`, show :
`int_(0)^(pi)cos^(2)mxdx={{:((pi)/(2),"when",mne0),(pi,"when",m=0):}`

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS|61 Videos

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS|58 Videos

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise MCQ EXERCISE 9A|15 Videos

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos

  • DEFINITE INTEGRAL AS AN AREA

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi)cos^(5)xdx=0

If m and n are positive integers and m ne n , show : int_(0)^(pi)cosmxcosnxdx=0

If m and n are positive integers and m ne n , show : int_(0)^(2pi)sinmxsinnxdx=0

int_(0)^(pi)xsinxcos^(2)xdx=(pi)/(3)

int_(0)^(pi)xcosxdx=-2

int_(0)^((pi)/(2))cos^(5)xdx=(8)/(15)

Prove that int_(-pi)^(pi)cosmxcosnxdx={{:(0,"when",mnen ne0),(pi,"when",m=n ne0),(2pi,"when",m=n=0):}

If m and n are integers and m ne n , then show that, int_(0)^(pi) sin mx cos nx dx={{:((2m)/(m^(2)-n^(2)),"when"(m-n)" is odd"),(0,"when"(m-n)"is even"):}

If n(ne0) is a positive integer then the value of int_(0)^(pi)cosnxdx is-

Evaluate: int_(0)^((pi)/(2))cos^(2)xdx