Exam 3 and Beyond

1First Fundamental Theorem of Calculus

1.1What’s in a calculus problem?

Two young mathematicians discuss what calculus is all about.

1.2The First Fundamental Theorem of Calculus

The rate that accumulated area under a curve grows is described identically by that curve.

2Second Fundamental Theorem of Calculus

2.1A secret of the definite integral

Two young mathematicians discuss what calculus is all about.

2.2The Second Fundamental Theorem of Calculus

The accumulation of a rate is given by the change in the amount.

2.3A tale of three integrals

At this point we have three ‘‘different’’ integrals.

3The idea of substitution

3.1Geometry and substitution

Two students consider substitution geometrically.

3.2The idea of substitution

We learn a new technique, called substitution, to help us solve problems involving integration.

4Working with substitution

4.1Integrals are puzzles!

Two young mathematicians discuss how tricky integrals are puzzles.

4.2Working with substitution

We explore more difficult problems involving substitution.

5Applications of integrals

5.1Applications of integrals

We give more contexts to understand integrals.

5.2Integration with substitution Exercises

Here we’ll practice finding integration with substitution.

5.3Area Between Curves Exercises

Here we’ll practice finding area between curves.

5.4Volume Exercises

Here we’ll practice finding volume using integration.

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