The value of the definite integral `int_0^1( x^2+1)dx`

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

The value of the definite integral int_0^1(x\ dx)/ (x^3+16) lies in the interval [a,b]. Then smallest such interval is

If the value of the definite integral int_0^1 "^(207)C_7x^(200)(1-x)^7dx is equal to 1/k ,w h e r ek in N , then the value of k/(26) is____

The value of the definite integral int_0^(pi/2) (dx)/(tanx+cotx+cosecx+secx) is

Evaluate the definite integrals int_0^1x e^(x^2)dx

The value of the definite integral int_0^(pi/2) ((1+sin3x)/(1+2sinx)) dx equals to

The value of the definite integral int_(0)^(1)(1+e^(-x^(2))) dx is

If the value of the definite integral int_0^1(sin^(-1)sqrt(x))/(x^2-x+1)dx is (pi^2)/(sqrt(n)) (where n in N), then the value of n/(27) is

The value of the definite integral int_(0)^(2) (sqrt(1+x ^(3))+""^(3) sqrt(x ^(2)+ 2x)) dx is :

The value of the definite integral int _(0) ^(10) ((x-5) +(x-5)^(2) +(c-5)^(3)) dx is: