How would you prove the 'integration by parts' rule?
This involves thinking about a well-known formula (the product rule) in a slightly different way. Looking at the product rule, for two functions u and v, (uv)' = uv' + vu'. We can rewrite this as uv' = (uv)' - vu'. Integrating both sides, we obtain integral of uv' = uv - integral of vu'.
ER
Related STEP University answers
All answers ▸Show that i^i = e^(-pi/2).
Find h(x), for x≠0, x≠1, given that: h(x)+h(1/(1−x))=1−x−1/(1−x)
Given a differential equation (*), show that the solution curve is either a straight line or a parabola and find the equations of these curves.
Show that substituting y = xv, where v is a function of x, in the differential equation "xy(dy/dx) + y^2 − 2x^2 = 0" (with x is not equal to 0) leads to the differential equation "xv(dv/dx) + 2v^2 − 2 = 0"