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Category: Integration

Integration by parts | Exercises

Practice, practice, practice. Theory is not everything. You need to apply what you learn from reading. These exercises will help you improve your “integration skills” by putting into practice what you’ve leant here https://addjustabitofpi.com/integration-techniques-integration-by-parts/ about integration by parts. If you don’t remember the basic integrals and their rules, click on these two links: https://addjustabitofpi.com/2019/10/03/fundamental-integrals/ https://addjustabitofpi.com/2019/10/03/rules-and-properties-of-integrals/. Check your results here: https://addjustabitofpi.com/2019/10/09/integration-by-parts-solution-with-procedure/.

U-substitution | Exercises

Here are some indefinite integrals you can practice with using u-sub. If you can’t solve all of them, don’t discourage. You can see the procedure for each here: https://addjustabitofpi.com/category/solutions/. This will help you understand the logics of integrals and you will eventually get the hang of it and be able to solve them right away! If you don’t remember the rules and properties of integrals, click this link: https://addjustabitofpi.com/rules-and-properties-of-integrals/. Notice that cot (cotangent) is the reciprocal of tan (tangent), which means that cot(x)=cos(x)/sin(x). Remember that sec (secant) is the reciprocal… Read more U-substitution | Exercises

What’s integration?

What’s the area of a rectangle? Easy! Width times height. Another one: what is the area of a circle? Yes! pi times the radius squared. What’s the area under a parabola? Easy!… well, not really (for now!). This is a graph of the function f(x) = x². The region in red is the area we want to calculate, and as you can see it’s bound between x=0.5 and x=1. That’s not a shape we know. It is not a circle nor a rectangle nor a triangle. It does look like… Read more What’s integration?

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