Given a real-valued function f which is monotonic and differentiable. Then `int_(f(a))^(f(b))2x(b-f^(-1)(x))dx=`

int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=

For every function f (x) which is twice differentiable , these will be good approximation of int_(a)^(b)f(x)dx=((b-a)/(2)){f(a)+f(b)} , for more acutare results for cin(a,b),F( c) = (c-a)/(2)[f(a)-f( c)]+(b-c)/(2)[f(b)-f( c)] When c= (a+b)/(2) int_(a)^(b)f(x)dx=(b-a)/(4){f(a)+f (b)+2 f ( c) }dx Good approximation of int_(0)^(pi//2)sinx dx , is

For every function f (x) which is twice differentiable , these will be good approximation of int_(a)^(b)f(x)dx=((b-a)/(2)){f(a)+f(b)} , for more acutare results for cin(a,b),F( c) = (c-a)/(2)[f(a)-f( c)]+(b-c)/(2)[f(b)-f( c)] When c= (a+b)/(2) int_(a)^(b)f(x)dx=(b-a)/(4){f(a)+f (b)+2 f ( c) }dx If lim_(t toa) (int_(a)^(t)f(x)dx-((t-a))/(2){f(t)+f(a)})/((t-a)^(3))=0 , then degree of polynomial function f (x) atmost is

If f is continuously differentiable function then int_(0)^(1.5) [x^2] f'(x) dx is

int_a^b[d/dx(f(x))]dx

If f(x) is monotonic differentiable function on [a,b], then int_(a)^(b)f(x)dx+int_(f(a))^(f(b))f^(-1)(x)dx=(a)bf(a)-af(b)(b) bf (b)-af(a)(c)f(a)+f(b)(d) cannot be found