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## Integration by Parts

Learn how to evaluate integrals where the integrand is a product of functions Integration by parts is a hugely helpful technique which greatly extends the number of functions that can be integrated. Like the product rule for differentiation, it allows us to integrate...

## Proof by Induction

Learn how to use proof by induction by following this example FollowFollowFollow All Mathematical theorems, formulas and rules have to be proven to be true. Mathematical proofs – demonstrations that a rule or theorem is true – can be straight-forward or...

## The Area Under a Curve

Learn how to find the area under a curve using definite integrals Finding the area underneath a curve is a common application of definite integrals. If you’re taking a course in integral Calculus you will almost certainly be asked to find the area underneath a...

## Evaluating Definite Integrals

Learn how to evaluate definite integrals using The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus is a key result in Mathematics. It essentially links together the two branches of Calculus, differentiation and integration (anti-differentiation)....