What is the fundamental theorem of calculus?

Problem Statement

What is the fundamental theorem of calculus?

Step-by-Step Explanation

The fundamental theorem of calculus connects derivatives and integrals as inverse processes.

1. Identify what the question is asking. In Calculus, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Final Answer

The fundamental theorem of calculus connects derivatives and integrals as inverse processes. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.