The value of `sum_(n=1)^100 int_(n-1)^n e^(x-[x])dx = `

The value of sum_(n=1)^1000 int_(n-1)^n e^(x-[x])dx , where [x] is the greatest integer function, is (A) (e^1000-1)/1000 (B) (e-1)/1000 (C) (e^1000-1)/(e-1) (D) 1000(e-1)

Evaluate sum_(n=1)^(1000)int_(n-1)^(n)|cos2pix|dx

Find the value of sum_(n=8)^100[{(-1)^n*n)/2] where [x] greatest integer function

The value of integral sum _(k=1)^(n) int _(0)^(1) f(k - 1+x) dx is

If x^(2)-x+1=0 then the value of sum_(n=1)^(5)[x^(n)+(1)/(x^(n))]^(2) is:

For x in Rwith|x|<1, the value of sum_(n=0)^(oo)(1+n)x^(n) is

If f(x) is continuous for all real values of x, then sum_(r=1)^(n)int_(0)^(1)f(r-1+x)dx is equal to (a)int_(0)^(n)f(x)dx(b)int_(0)^(1)f(x)dx(c)int_(0)^(1)f(x)dx(d)(n-1)int_(0)^(1)f(x)dx

The value of the integral int_0^1 x(1-x)^n dx=