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intm^n x dx...

`int_m^n x dx`

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Explore conceptually related problems

Evaluate : int_( 0 )^n x - [ x ] dx

A periodic function with period 1 is integrable over any finite interval.Also,for two real numbers a,b and two unequal non-zero positive integers m and nint_(a)^(a+n)f(x)dx=int_(b)^(b+m)f(x) calculate the value of int_(m)^(n)f(x)dx

Knowledge Check

  • If overset(a)underset(0) int f(2a-x)dx = m and overset(a)underset(0)int f(x) dx=n , then overset(2a)underset(0) int f(x) dx is equal to

    A
    `2m+n`
    B
    `m+2n`
    C
    `m-n`
    D
    `m+n`

  • Let n in N such that n gt 1 . Statement-1: int_(oo)^(0) (1)/(1+x^(n))dx=int_(0)^(1) (1)/((1-x^(n))^(1//n))dx Statement-2: int_a^b f(x)dx=int_(a)^(b) f(a+b-x)dx

    A
    Statement-1 is true, Statement-2 is True,Statement-2 is a correct explanation for Statement-1.
    B
    Statement-1 is True, Statement-2 is not a correct explanation for Statement-1.
    C
    Statement-1 is True, Statement-2 is False.
    D
    Statement-1 is False, Statement-2 is True.

  • Evaluate : int x^n log x dx.

    A
    `(x)/(nm +1) [ log x - (1)/((n +1))] +C`
    B
    ` (x^(n+1))/(nm +1) [ log x - (1)/((n +1))] +C`
    C
    `(x^(n+1))/(n +1) [ log x - (1)/((n +1))] +C`
    D
    `(x^(n+1))/(nm ) [ log x - (1)/((n +1))] +C`

    • Similar Questions

    Explore conceptually related problems

    Property 13:int_(mT)^(nT)f(x)dx=(n-m)int_(0)^(T)f(x)dx where T is period of f(x) and m and n are integer

    If (d)/(dx)[ x^(n+1)+c]=(n+1)x^(n) , then find int x^(n)dx .

    If for every integer n, int_(n)^(n+1) f(x) dx= n^(2) , then the value of int_(-2)^(-4) f(x) dx is

    If int_(0)^(1) x^(m) (1-x)^(n) dx= R int_(0)^(1) x^(n) (1-x)^(m) dx , then

    If I_(m,n)= int_(0)^(1) x^(m) (ln x)^(n) dx then I_(m,n) is also equal to

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