If `(x)` is of the form `f(x)=a+b x+c x^2,` show that `int_0^1f(x)dx=1/6{f(0)+4f(1/2)+f(1)}`

If (x) is of the form f(x)=a+bx+cx^(2) show that int_(1)f(x)dx=(1)/(6){f(0)+4f((1)/(2))+f(1)}

If f(x)=a+bx+cx^(2) , show that, int_(0)^(1)f(x)dx=(1)/(6)[f(0)+4f((1)/(2))+f(1)]

Evaluate the following: If f(x)= a + bx + c x^2 , show that \int_{0}^1 f(x) = (1/6)[f(0) + 4f(1/2) + f(1)]

If f(x) is of the form f(x) = a + bx + cx^2 , show that underset(0)overset(1)intf(x) dx = 1/6 [f(0)+4f(1/2)+f(1)]

If f(x) is a quadratic polynomial in x such that 6int_0^1 f(x)dx-{f(0)+4f((1)/(2))}=kf(1) , then k=

If f(x) is a quadratic polynomial in x such that 6int_0^1 f(x)dx-{f(0)+4f((1)/(2))}=kf(1) , then k=

If f(x)=1+x^(2)+x^(4)+x^(6)+…..oo then int_(0)^(x)f(x)dx=

(A) For each of the following function f(x), verify that: int_0^2 f(x) dx=int_0^1 f(x) dx+int_1^2 f(x) dx: (i) f(x)=x+2 (ii) f(x)= x^2+2 (iii) f(x)= e^x (B) For each of the following pairs of function f(x) and g(x) , verify that: int_0^1 [f(x)+g(x)]dx=int_0^1 f(x) dx+int_0^1 g(x) dx: (i) f(x)=1,g(x) = x^2 (ii) f(x)=e^x, g(x)=1

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx