Laplace TransformsExpected Educational ResultsImproper IntegralsThe Tanzalin Method for Integration by PartsImproper IntegralsImproper IntegralsCC BY-NC-SA 4.0

**Author**: John J Weber III, PhD
**Corresponding Textbook Sections**:

**Section 7.2**– Definition of the Laplace Transforms

**Objective 4–1**: I can evaluate an indefinite trigonometric integral.**Objective 4–2**: I can evaluate a definite trigonometric integral using FTC-II.

**Example 01a**: Integrate

**Solution**:

**Multiply** along the diagonals and **multiply** with sign along diagonals.

**Example 01b**: Integrate

**Solution**:

Rewrite all terms:

Use *l’Hopital’s Rule* to evaluate the first two limits:

Evaluate the limits:

**Example 02a**: Integrate

**Multiply** along the diagonals and **multiply** with sign along diagonals. **Multiply** along the the last horizontal and **integrate** the product.

**Combine** the integrals:

**Solve** for the integral:

**Example 02b**: Integrate

**Solution**:

Rewrite all terms:

Evalaute the limit:

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**Last Modified**: Sunday, November 2020 8:59 EDT