Definite integrals

5 videos
2 skills
Until now, we have seen definite integrals as the area under a curve. We've approximated this area with reactangles using Riemann sums. We also realized that we could potentially find the exact area if we take the limit as we approach having an infinite, infinitely thin rectangles. But is there an easier way to evaluate an integral? Even more, does this somehow connect to everything we know about the derivative and differential calculus? Hold on to your seats, because everything is about to come together!

Riemann sums and integrals

VIDEO 4:26 minutes

Connecting the first and second fundamental theorems of calculus

VIDEO 4:45 minutes

Intuition for second fundamental theorem of calculus

VIDEO 12:24 minutes

Evaluating simple definite integral

VIDEO 5:54 minutes

Area between a curve and an axis

PRACTICE PROBLEMS

Definite integrals and negative area

VIDEO 7:28 minutes

Evaluating definite integrals

PRACTICE PROBLEMS
Evaluating definite integrals using the fundamental theorem of calculus