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.