# Fundamental Theorem of Calculus

- The two major branches of calculus have been introduced:
- differential calculus
- integral calculus.

- At this point, these two problems might seem unrelatedâ€”but there is a very close connection.
- The connection was discovered independently by Isaac Newton and Gottfried Leibniz and is stated in a theorem that is appropriately called the
**Fundamental Theorem of Calculus**. - Informally, the theorem states that differentiation and (definite) integration are inverse operations, in the same sense that division and multiplication are inverse operations.
- The slope of the tangent line was defined using the slope of the secant line.
- Similarly, the area of a region under a curve was defined using the area of a rectangle.
- So, at least in the primitive approximation stage, the operations of differentiation and definite integration appear to have an inverse relationship in the same sense that division and multiplication are inverse operations.
- The Fundamental Theorem of Calculus states that the limit processes used to define the derivative and definite integral preserve this inverse relationship.

## Essential Questions

Essential Questions

### How are definite integrals evaluated using the Fundamental Theorem of Calculus?

How are definite integrals evaluated using the Fundamental Theorem of Calculus?