`int_-r^r pi(r^2-x^2)dx`

Q. if int_0^100(f(x) dx = a , then sum_(r=1)^100(int_0^1( f(r-1+x)dx)) =

Integrate the following functions int_(0)^(r ) (2x-x^(3)) dx

solve int_(pi/4)^(pi/2) x^2 dx

[ The value of int_(-pi)^( pi)sum_(r=0)^(999)cos rx(1+sum_(r=1)^(999)sin rx) dx, is [ (1) 2 pi, (2) 999 pi, (3) 0]]

Let f: R rarr R be a continuous function given by f(x+y)=f(x)+f(y) for all x,y, in R, if int_0^2 f(x)dx=alpha, then int_-2^2 f(x) dx is equal to

If int_(0)^(100) f(x)dx=7, then sum_(r=1)^(100)int_(0)^(1)f(r-1+x)dx= _________.

Solve the integral I=int_oo^R(GMm)/(x^2)dx .

Let g(x) be differentiable on R and int_(sint)^1x^2g(x)dx=(1-sint), where t in (0,pi/2)dot Then the value of g(1/(sqrt(2))) is____

Let g(x) be differentiable on R and int_(sint)^1x^2g(x)dx=(1-sint), where t in (0,pi/2)dot Then the value of g(1/(sqrt(2))) is____

int_(2-a)^(2+a)f(x)dx is equal to [where f(2-alpha)=f(2+alpha) AAalpha in R (a) 2 int_2^(2+a)f(x)dx (b) 2int_0^af(x)dx (c) 2int_2^2f(x)dx (d) none of these