Calculate Integrals
Calculate Indefinite Integrals
Calculate Indefinite Integrals
Example
Solve:
Integration using completing the square
![](https://solomons-mathbook.gitbook.io/~gitbook/image?url=https%3A%2F%2Fuser-images.githubusercontent.com%2F14041622%2F42393904-be29c282-818a-11e8-92e7-eb5b467c775d.png&width=768&dpr=4&quality=100&sign=d6c88d3e&sv=1)
Example
Solve:
Rewrite it to this form:
Use the special arctan rule to solve it, and get:
Example
Solve: Solve:
Rewrite it to this form:
Use the special arctan rule to solve it, and get:
Calculate Definite Integrals
Calculate Definite Integrals
Example
Solve: Don't get confused when you see the Upper boundary is smaller than the Lower one.
![](https://solomons-mathbook.gitbook.io/~gitbook/image?url=https%3A%2F%2Fuser-images.githubusercontent.com%2F14041622%2F41094263-4493ee8c-6a80-11e8-8bcd-54ba5f991181.png&width=768&dpr=4&quality=100&sign=a4b403f7&sv=1)
Example (piecewise integration)
Example (Absolute value)
Solve:
Splitting up the absolute value, and notice that the absolute value function is a piecewise function. Here we have that:
Splitting up the definite integral:
Evaluating each piece:
Answer is 20.
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