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  2. AP Calculus
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What is the Integration by Parts formula?

∫u,dv=uv−∫v,du\int u , dv = uv - \int v , du∫u,dv=uv−∫v,du

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What is the Integration by Parts formula?

∫u,dv=uv−∫v,du\int u , dv = uv - \int v , du∫u,dv=uv−∫v,du

What is the product rule for differentiation?

ddxuv=ucdotv′+vcdotu′\frac{d}{dx} uv = u cdot v' + v cdot u'dxd​uv=ucdotv′+vcdotu′

What are the differences between u-substitution and Integration by Parts?

u-substitution: Reverses the chain rule, simplifies composite functions. | Integration by Parts: Reverses the product rule, simplifies products of functions.

What is Integration by Parts?

A technique to integrate the product of two functions, based on the product rule for differentiation.

Define 'u' in Integration by Parts.

A selected part of the integrand that is differentiated.

Define 'dv' in Integration by Parts.

A selected part of the integrand that is integrated.

What is 'du' in Integration by Parts?

The derivative of 'u' with respect to the variable of integration.

What is 'v' in Integration by Parts?

The antiderivative (integral) of 'dv'.