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:

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_____

If P(x) is a polynomial of degree 3 satisfying p(-1)=10 ,p(1)=-6a n dp(x) has maxima at x=-1a n dp^(prime)(x) has minima at x=1, find the distance between the local maxima and local minima of the curve.

int_(1)^(2)x^(2)dx is equal to

p(x) is a polynomial of degree 1 and q(x) is a polynomial of degree 2. What kind of the polynomial p(x) xx q(x) is ?

f(x) is polynomial function of degree 6, which satisfies ("lim")_(xvec0)(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. Column I, Column II The coefficient of x^6 , p. 0 The coefficient of x^5 , q. 2 The coefficient of x^4 , r. -(12)/5 The coefficient of x^3 , s. 2/3

consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1 and lim_(xrarr0) p(x)/(x^(3))-2=4 Then the value of P(x)_____.

int sqrt(e^(x)-1)dx is equal to

int(x^3-x)/(1+x^6)dx is equal to