Example 5

EXAMPLE 5

The only way we can show that the function has an antiderivative is to take a definite integral

This is a "new" function that cannot be expressed in terms of algebraic, trigonometric, and exponential functions without calculus.

The Fundamental Theorem can also be used to find the derivative of a function which is defined as a definite integral with a variable limit of integration. This can be done without actually evaluating the integral.