1. Integration: The General Power Formula

by M. Bourne

In this section, we apply this formula to trigonometric, logarithmic and exponential functions:

math expression

(We met this substitution formula in an earlier chapter: General Power Formula for Integration.)

Example 1: Integrate: math expression


Answer

Example 2: Integrate: math expression


Answer

Example 3: Integrate: math expression


Answer

Example 4: Integrate: math expression


Answer

Example 5: Find the equation of the curve for which math expression if the curve passes through (1,2).


Answer

 

Exercises

Integrate each of the following functions:

1. math expression


Answer

2. math expression


Answer

3. math expression


Answer

4. math expression


First, the LiveMath solution to this problem.

LIVEMath


Answer

5. Find the equation of the curve for which math expression if the curve passes through (2,1).


Answer

6. A space vehicle is launched vertically from the ground such that its velocity v (in km/s) is given by

math expression

where t is the time in seconds. Find the altitude of the vehicle after 10.0 s.

The graph of math expression is as follows:

math expression


Answer



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