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.`

Find the value of int_0^1x(1-x)dx

Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The value of P(0) is

Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The value of P(2) ius

Consider a polynomial y = P(x) of the least degree passing through A(-1,1) and whose graph has two points of inflection B(1,2) and C with abscissa 0 at which the curve is inclined to the positive axis of abscissa at an angle of sec^(-1)sqrt(2) The equation P(x) =0 has

Find the value of int_0^1{(sin^(-1)x)//x}dx

Find the points on the curve x y+4=0 at which the tangents are inclined at an angle of 45^@ with the x-axis.

Find the points on the curve x y+4=0 at which the tangents are inclined at an angle of 45^0 with the x- axis .

The tangent, represented by the graph of the function y=f(x), at the point with abscissa x = 1 form an angle of pi//6 , at the point x = 2 form an angle of pi//3 and at the point x = 3 form and angle of pi//4 . Then, find the value of, int_(1)^(3)f'(x)f''(x)dx+int_(2)^(3)f''(x)dx.

Find the value of the following: int_0^1 dx/(1+x^2)

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)=6a n dp(3)=2, then p^(prime)(0) is_____