Let `P(x)` be a polynomial of least degree whose graph has three points of inflection `(-1,-1),(1.1) `and a point with abscissa 0 at which the curve is inclined to the axis of abscissa at an angle of `60^@.` Then find the value of`int_0^1 p(x)dx.`

The tangent to the graph of the function y=f(x) at the point with abscissa x=a forms with the x-axis an angle of (pi)/(3) and at the point with abscissa x=b at an angle of (pi)/(4) then the value of the integral,int_(1)^(b)f'(x)*f''(x)dx is equal to

Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3. If p(1)=6 and p(3)=2, then p'(0) is

Let P(x) be a polynomial of degree 11 such that P(x)=(1)/(x+1), for x=0,1,2,...11. The value of P(12) is

If P(x) is a polynomial of the least degree that has a maximum equal to 6 at x=1, and a minimum equalto 2 at x=3, then int_(0)^(1)P(x)dx equals:

P(x) be a polynomial of degree 3 satisfying P(-1) =10 , P(1) =-6 and p(x) has maxima at x = -1 and p(x) has minima at x=1 then The value of P(1) is