Let’s now look at the substitution method, also known as u-substitution. The c term represents a constant value that is a result of integration and should never be forgotten, especially on multiple choice questions of the AP® Calculus exam. Next, we integrate each term, adding one to the exponent and dividing the answer by the new exponent value: So we set up the integral, keeping in mind the dx term: Instead of subtracting one from the exponent, you add one, and instead of multiplying the quantity by the new exponent, you divide it. The anti-chain rule method is basically the reverse of the chain rule method implemented in the derivative section of your textbook. We are now moving on to the fun part: seeing some examples. Solving an indefinite integral is the same thing as solving for the antiderivative, or undoing the derivative and solving for the original function. Indefinite integrals can be solved using two different methods, the anti-chain rule method and the substitution method. Indefinite integrals will be addressed first, since the method for solving them is also used as a part of calculating definite integral solutions. A definite integral has bounds and yields a numerical answer, while an indefinite integral does not have bounds and yields an algebraic answer.
Integrals can be split into two separate categories: definite and indefinite. Reading this AP® Calculus review will outline all the tools you need, and hopefully calm the butterflies in your stomach. In order to help quell your fears, I will walk you through the most important concepts of solving even the most challenging of integrals. Integration may be the most challenging concept in AP® Calculus textbooks, but it is also arguably the most important! That being said, there is no shame in being nervous for the upcoming AP® exam.
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