Evaluating Definite Integrals with the FTC

Calculus 1 · Axiom Academy

EXAMPLE Evaluating Definite Integrals with the FTC Apply the Fundamental Theorem of Calculus to compute an exact definite integral, step by step. Evaluate the definite integral using the Fundamental Theorem of Calculus, Part 2. Nice work. You evaluated a definite integral end to end with the Fundamental Theorem of Calculus, Part 2. FTC, Part 2: , where F is any antiderivative of f . No +C needed: for a definite integral the constant of integration cancels in the subtraction, so you can drop it. Bracket notation: is just shorthand for "evaluate F at b , then subtract its value at a ." The FTC links the antiderivative to area: instead of summing infinitely many rectangles, you find one antiderivative and subtract two numbers.

This is the written version of the interactive lesson above. See the full Calculus 1 course.