Home
Class 12
MATHS
If f(x) is polynomaial function of degre...

If `f(x)` is polynomaial function of degree n, prove that `int e^x f(x) dx=e^x[f(x)-f '(x)+f''(x)-f'''(x)+......+(-1)^n f^n (x)]` where `f^n(x)=(d^nf)/(dx^n)`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

If f(x)is integrable function in the interval [-a,a] then show that int_(-a)^(a)f(x)dx=int_(0)^(a)[f(x)+f(-x)]dx.

int [f(x)g"(x) - f"(x)g(x)]dx is

The value of int e^(x)[f(x)+f'(x)]dx is equal to -

Let f(x) be the polynomial of degree n, then Delta^(n-1) f(x) is a polynomial of degree.

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

If int(e^x-1)/(e^x+1)dx= f(x) +c, then find f(x).

If f(x)=(a-x^(n))^(1/n),agt0 and n is a positive integer, then prove that f(f(x)) = x.

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

f(x) is polynomial function of degree 6, which satisfies ("lim")_(x_vec_0)(1+(f(x))/(x^3))^(1/x)=e^2 and has local maximum at x=1 and local minimum at x=0a n dx=2. then 5f(3) is equal to