Selecting Techniques for Antidifferentiation (AB)

#6.14 Selecting Techniques for Antidifferentiation

In AP Calculus, we encounter a variety of functions, and each may require a different approach for antidifferentiation. This skill is all about choosing the right technique or method to find the antiderivative of a given expression. Let's explore the techniques necessary for this task in detail! 🚀

#🔋Power Rule for Antiderivatives

The power rule for antiderivatives is a fundamental technique used to find the antiderivative of a function raised to a power. When you have an integral in the form ∫$x^n dx$, this rule is your go-to method. It states that if you have$\int x^n dx$, where n is not equal to -1, you add 1 to the exponent and divide by the new exponent. This results in:

$$\int x^n dx=\frac{x^{n+1}}{(n+1)} + C$$

Where C is the constant of integration.

#🚇 U-substitution (U-sub)

U-substitution is a powerful technique for simplifying complex integrals. It involves substituting a portion of the expression with a single variable (usually denoted as 'u') to make the integral more manageable.

This method is particularly useful when dealing with composite functions o...