If `int_a^bf(x)dx=((b-a)lambda)/8int_0^1f((b-a)x+a)dx` then the value of `lambda` is

int_(a)^( If )f(x)dx=((b-a)lambda)/(8)int_(0)^(1)f((b-a)x+a)dx

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

If int_0^(a) f(x) dx = int_0^(a) f(a-x) dx , then the value of int_0^(pi) x. f(sin x) dx =

If int (dx)/(1+sinx) = tan (x/2 - pi/lambda) + b , then the value of lambda is -

If |int_(a)^(b)f(x)dx|=int_(a)^(b)|f(x)|dx,a

Suppose in the definite integral int_a^b f(x) dx the upper limit b->oo, then to obtain the value of int_a^bf(x) dx , we may say that int_a^bf(x)dx=lim_(k->oo)int_a^k dx, where k > a. if f(x)->oo as x ->a or x->b, then the value of definite integral int_a^bf(x)dx is lim_(h->0) int_(a+h)^b f(x) dx. If this limit the value of the limit is defined as the value of integral. This should be noted that f (x)should not have any other discontinuity in [a, b] otherwise this will lead to errorous solution.