" 35."f(xdx)/((x-a)(x-b))

int (xdx)/((x-a)(x-b))

If f(x)=b(x-a)/(b-a)+a(x-b)/(a-b) ,show that f(a)+f(b)=f(a+b).

int (xdx)/((x^(2)-a^(2))(x^(2)-b^(2)))=

int (xdx)/((x^(2)+b^(2))

{:("Column A" , "A function f(x) is defined for all real numbers as","Column B"),(, f(x)=(x - 1)(x-2)(x-3)(x-4),),( f(2.5), ,f(3.5)):}

If f(x)=(b(x-a))/(b-a)+(a(x-b))/(a-b), prove that f(a+b)=f(a)+f(b)

Verify Lagrange's mean value theorem for the function f(x) in the interval [3,5] where f(x) =(x-3)(x-6)(x-9)

If f(x)=(a(x-b))/(a-b)+(b(x-a))/(b-a) , then prove that f(a) + f(b) = a + b.