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Infinite Intervals of Integration

Infinite Intervals of Integration. Objectives. Students will be able to Use limits to determine if infinite intervals of integration are convergent or divergent. Calculate improper integrals (where possible). Improper Integrals.

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Infinite Intervals of Integration

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  1. Infinite Intervals of Integration

  2. Objectives Students will be able to • Use limits to determine if infinite intervals of integration are convergent or divergent. • Calculate improper integrals (where possible).

  3. Improper Integrals

  4. When the limit of an improper integral exists, then the integral is said to be convergent. If the limit of an improper integral does not exist, then the integral is said to be divergent.

  5. Example 1 Find the area, if it is finite, of the region under the graph of over the interval

  6. Example 2 Determine whether the improper integral below converges or diverges. If it converges, find the value.

  7. Example 3 Determine whether the improper integral below converges or diverges. If it converges, find the value.

  8. Example 4 Determine whether the improper integral below converges or diverges. If it converges, find the value.

  9. Example 5 Find if possible

  10. Example 6 An investment produces a perpetual stream of income with a flow rate of Find the capital value at an interest rate of 10% compounded continuously.

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