Integration Techniques Tutor Help
Beyond the power rule: u-substitution runs the chain rule backwards, integration by parts trades a hard integral for an easier one, and both unlock area between curves and volumes of revolution.
1 Concept recap
The essentials of Integration Techniques & Applications, on one screen.
u-sub
u = inner function; du must appear (up to a constant) in the integrand. Change bounds or back-substitute for definite integrals.
By parts
∫ u dv = uv − ∫ v du. Choose u by LIATE so differentiating it simplifies the new integral.
Applications
Area = ∫(top − bottom); volume (disks) = π∫R². Radius = distance from region to axis — draw it first.
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