Grade 12Discuss with colleagues and IITians
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 as
fg = (fg) - f g
and integrating both sides tells us
This 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. Then and g(x) = x.
We can conclude that the integral of ln(x) from a to b is bln(b) - aln(a) - (b - a).
