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Week 3: Integration

Net Change Theorem

The integral of a rate of change is the net change:

Table of Indefinite Integrals

Evaluate the definite integrals. Show your work.

38.

46.

58. The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = . Find the area of this region by writing x as a function of y and integrating withrespect to y.

Question 68

The graph shows the velocity (in m/s) of an electric autonomous vehicle moving along a straight track. At t = 0 the vehicle is at the charging station.

1. How far is the vehicle from the charging station when t = 2, 4, 6, 8, 10, and 12?

2. At what times is the vehicle farthest from the charging station?

3. What is the total distance traveled by the vehicle?

The Substitution Rule

If u = g(x) is differentiable on an interval I and f is continuous on I, then

Evaluate the indefinite integrals (use substitution when helpful).

6.

16.

36.