Integration by u-substitution

The  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:


 * 1) Find the definite integral: This problems has a definite integral that involves a substitution. The student is expected to find the correct value of the integral and indicate the answer as required.Ibus1.png
 * 2) Find the indefinite integral: This problem has an indefinite integral that involves a substitution. The student is expected to find the correct antiderivative and select it from a multiple choice list.Ibus2.png
 * 3) Apply integral properties: This problem has an abstract integral that involves substitution. The student is expected to make the correct substitution and use the resulting expression to find the value requested.Ibus3.png

Strategies
Knowledge of derivatives, recognizable antiderivatives and integral properties are encouraged to ensure success on this exercise.
 * 1) These are called u-substitution because the way they are taught generally uses the variable u as the substitution name.
 * 2) Once u is chosen, the du and the bounds can bother be replaced to change the integral.
 * 3) 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.
 * 4) To increase efficiency one should recognize power rules and other basic derivatives and integrals.

Real-life Applications

 * 1) Integral techniques are important for finding any integral that is not immediately set up as one that is recognizable.
 * 2) Integration has many applications in the sciences and economics to find "totals."