The product rule, says that the derivative of a product is the sum gotten by differentiating each factor as if the other were constant and adding up the results.We can read this backwards as a way to handle an integrand of the form fg, when we know how to handle the integrand f g. For, we can write the product rule asfg = (fg) - f gand integrating both sides tells usThis statement is called integrating by parts and is useful for integrands like xkexp(x) or ln(x) or xln(x).For example, to integrate ln(x), set f(x) = ln(x) and g(x)= 1. Thenand g(x) = x.We can conclude that the integral of ln(x) from a to b is bln(b) - aln(a) - (b - a).

Shiv , 11 Years ago

Grade 12