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/.
Here are the solutions with procedure of these integrals: https://addjustabitofpi.com/u-substitution-exercises/. If you don’t remember the rules and properties of integrals, check this out: https://addjustabitofpi.com/rules-and-properties-of-integrals/.
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 →
U-substitution is a very useful technique for integration. You can apply it in every case, but it doesn’t always make things easier. But here comes this new technique in help!… Read more Integration techniques | Integration by parts →
Ok, we now have the basis of integration! As I said in the previous post, I am now going to cover the techniques of integration. I will make a post… Read more Integration techniques | U substitution →
Ok, this is the second step! I will cover the rules you need to apply to calculate an integral. With the next lesson, you will hopefully be able to start… Read more Rules and properties of integrals →
In order to be able to solve integrals, (whether they are definite of indefinite) you need to learn the fundamental integrals first, the same way you did for the derivatives.… Read more Fundamental integrals →
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? →