`int_n^(n+1)f(x) dx=n^2+n` then `int_(-1)^1 f(x) dx =`

int_(0)^(a)f(2a-x)dx=m and int_(0)^(a)f(x)dx=n then int_(0)^(2a)f(x)dx is equal to

Suppose for every integer n, .int_(n)^(n+1) f(x)dx = n^(2) . The value of int_(-2)^(4) f(x)dx is :

For every integer n, int_(n)^(n+1)f(x)dx=n^(2) , then the value of int_(0)^(5)f(x)dx=

If n in N , then int_(-n)^(n)(-1)^([x]) dx equals

Statement-1: int_(0)^(npi+v)|sin x|dx=2n+1-cos v where n in N and 0 le v lt pi . Stetement-2: If f(x) is a periodic function with period T, then (i) int_(0)^(nT) f(x)dx=n int_(0)^(T) f(x)dx , where n in N and (ii) int_(nT)^(nt+a) f(x)dx=int_(0)^(a) f(x) dx , where n in N

f(x) is a continuous function for all real values of x and satisfies int_(n+1)^(n+1)f(x)dx=(n^(2))/(2)AA n in I. Then int_(5)^(5)f(|x|)dx is equal to (19)/(2) (b) (35)/(2) (c) (17)/(2) (d) none of these

If n in N, then int_(-n)^(n)(-1)^([x])dx equals

Which of the following are true ?(i)int_(a)^( pi-a)xf(sin x)dx=(pi)/(2)int_(a)^( pi-a)f(sin x)dx( ii) int_(-a)^(a)f(x^(2))dx=2int_(0)^(a)f(x^(2))dx( iii) int_(0)^(n pi)f(cos^(2)x)dx=n int_(0)^( pi)f(cos x)dx,n in N (iv) int_(0)^(b-c)f(x+c)dx=int_(c)^(b)f(x)dx