How to Find the Antiderivative: A Comprehensive Guide

TLDRThe antiderivative is the opposite of differentiation and is found by integrating the function. It is denoted by capital F of x and can be found using the power rule and the constant of integration.

Key insights

🔍The antiderivative is the opposite of differentiation and is found by integrating the function.

🔢The antiderivative of a constant is the constant times the variable plus the constant of integration.

📈The power rule is used to find the antiderivative of a variable raised to a constant power.

🔀The antiderivative of a sum or difference of functions is the sum or difference of their antiderivatives.

⏲️Indefinite integrals do not have limits of integration, while definite integrals do.

Q&A

What is the antiderivative?

The antiderivative is the opposite of differentiation and is found by integrating the function.

How do you find the antiderivative of a constant?

The antiderivative of a constant is the constant times the variable plus the constant of integration.

What is the power rule?

The power rule is used to find the antiderivative of a variable raised to a constant power.

How do you find the antiderivative of a sum or difference of functions?

The antiderivative of a sum or difference of functions is the sum or difference of their antiderivatives.

What is the difference between an indefinite integral and a definite integral?

Indefinite integrals do not have limits of integration, while definite integrals do.

Timestamped Summary

00:00The antiderivative is the opposite of differentiation and is found by integrating the function.

05:00The power rule is used to find the antiderivative of a variable raised to a constant power.

10:00The antiderivative of a constant is the constant times the variable plus the constant of integration.

13:00The antiderivative of a sum or difference of functions is the sum or difference of their antiderivatives.

15:00Indefinite integrals do not have limits of integration, while definite integrals do.