| Integration by u-substitution | |
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| Description | |
| Exercise Name: | Integration by u-substitution |
| Math Missions: | Integral calculus Math Mission |
| Types of Problems: | 3 |
The Integration by u-substitution exercise appears under the Integral calculus Math Mission. This exercise practices integration by performing a substitution.
Types of Problems[]
There are three types of problems in this exercise:
- Find the definite integral: This problems has a definite integral that involves a substitution. The user is expected to find the correct value of the integral and indicate the answer as required.
Find the definite integral
- Find the indefinite integral: This problem has an indefinite integral that involves a substitution. The user is expected to find the correct antiderivative and select it from a multiple choice list.
Find the indefinite integral
- Apply integral properties: This problem has an abstract integral that involves substitution. The user is expected to make the correct substitution and use the resulting expression to find the value requested.
Apply integral properties
Strategies[]
Knowledge of derivatives, recognizable antiderivatives and integral properties are encouraged to ensure success on this exercise.
- These are called u-substitution because the way they are taught generally uses the variable u as the substitution name.
- Once u is chosen, the du and the bounds can bother be replaced to change the integral.
- Generally the correct u is the piece that is separate from the rest of the integrand, for example, in the denominator, in the exponent, or in the argument of a trig function.
- To increase efficiency one should recognize power rules and other basic derivatives and integrals.
Real-life Applications[]
- Integral techniques are important for finding any integral that is not immediately set up as one that is recognizable.
- Integration has many applications in the sciences and economics to find "totals."