integration by parts

• \(\int_a^b f'(t)g(t)dt = f(t)g(t) \big\vert_a^b - \int_a^b f(t)g'(t) dt\)
• this comes from the product rule: \(\frac{f(t)g(t)}{dt} = f'(t)g(t) + f(t)g'(t)\)
• useful when you need to "move the derivative" off of one function onto another