Student Resources

Unit X. Techniques of Antidifferentiation

Activities

1 TI-Inspire Activity: Integration by Parts
This is a TI activity for the TI-Inspire to teach Integration by Parts.

Games

2 Power Saucers Game
This game asks the user to shoot saucers with correct integrals to win points.

Tutorials

3 Change of Limits for Definite Integrals
This link provides a discussion of definite integrals and u-substitution.
4 Indefinite Integrals
This link shows a proof that antiderivatives are unique up to a constant.
5 U-Subsitution Example (Rational)
This provides an example of evaluating the integral of a rational function using u-substitution.
6 U-Substitution Example (sine)
This provides an example of evaluating an integral of a trigonometric function by means of u-substitution.

Unit XI. Applications of Antidifferentiation

1 Velocity and Position
This link contains a solution to a problem: given a polynomial describing an object's velocity and its initial position, what is a function describing the object's position as time changes?

Videocasts

2 Antiderivatives with Initial Conditions
This link contains RealMedia lessons to find antiderivatives given initial conditions.
3 Part 3: Antiderivative AAAA Definite Integral (DE streaming)
The Candy-Coated World of Calculus, Program 8: Practical Applications. Part 3 discusses the anti-derivative and the definite integral (Student Login: hcpss_student, Password: student).
4 Radioactive Decay
This link contains a RealMedialessons on exponential decay of radioactive material in rocks.
5 Section C: The Definite Integral (DE streaming)
The Candy-Coated World of Calculus, Program 9: The Anti-derivative. Section C discusses the definite integral (Student Login: hcpss_student, Password: student).
6 Separable Differential Equations
This link contains a RealMedia lesson on solving separable differential equations.

Unit XII. Properties of Definite Integrals

eTools

1 Approximation Techniques
This applet allows the user to experiment with left, right, and midpoint Riemann sums for functions the user enters, as well as inscribed rectangles, circumscribed rectangles, and the trapezoidal rule.

Tutorials

2 Approximating Area (Circumscribed Rectangles)
This tutorial provides animated directions for approximating the area under a particular function by using circumscribed rectangles.
3 Approximating Area (Inscribed Rectangles)
This tutorial provides animated directions for approximating the area under a particular function by using inscribed rectangles.
4 Average Rate of Change and Average Value
This tutorial compares the average value of a function with its average rate of change.
5 Definite Integral and Riemann Sums
This tutorial defines a definite integral as the limit of Riemann sums.
6 Fundamental Theorem Example (Absolute Value)
This tutorial shows an example of evaluating an integral involving an absolute value function.
7 Riemann Sums
This tutorial uses Riemann sums to evaluate a particular definite integral.
8 Upper and Lower Sums (Polynomial Graph)
This tutorial compares the estimates for the area under part of a parabola given by inscribed and circumscribed rectangles and includes an animated graph.
9 Upper and Lower Sums (Sine graph)
This tutorial compares the estimates for the area under part of a sine curve given by inscribed and circumscribed rectangles and includes an animated graph.

Videocasts

10 Fundamental Theorem of Calculus
This link contains RealMedia lessons on the Fundamental Theorem of Calculus.
11 Section D: Riemann Sums (DE streaming)
The Candy-Coated World of Calculus, Program 9: The Anti-derivative. Section D discusses Riemann Sums (Student Login: hcpss_student, Password: student).
12 Section E: The Fundamental Theorem of Calculus (DE streaming)
The Candy-Coated World of Calculus, Program 9: The Anti-derivative. Section E discusses the Fundamental Theorem of Calculus (Student Login: hcpss_student, Password: student).