Question

What is the proof for formula of integration by parts?

Answer 1

Answer:

Step-by-step explanation:

d(f(x)*g(x))/dx = f(x)*g'(x) + f'(x)*g(x)

We solve for f(x)*g'(x):

f(x)*g'(x) = d(f(x)*g(x))/dx - f'(x)*g(x)

Integrate both sides and recall that an integral is the

antiderivative:

INT[f(x) g'(x)dx] = f(x)*g(x) - INT[ f'(x) g(x) dx]

Then change to the common notation:

u = f(x)

v = g(x)

du = f'(x)dx

dv = g'(x)dx

This gives us the formula for integration by parts:

INT[u dv] = uv - INT[v du]

I hope that helped. ☺