Infinite Intervals of Integration

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Presentation transcript:

Infinite Intervals of Integration Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Objectives Students will be able to Use limits to determine if infinite intervals of integration are convergent or divergent. Calculate improper integrals (where possible). Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Improper Integrals Implicit Differentiation Properties of Definite Integrals Local Extreme Points

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. Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 1 Find the area, if it is finite, of the region under the graph of over the interval Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 2 Determine whether the improper integral below converges or diverges. If it converges, find the value. Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 3 Determine whether the improper integral below converges or diverges. If it converges, find the value. Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 4 Determine whether the improper integral below converges or diverges. If it converges, find the value. Implicit Differentiation Properties of Definite Integrals Local Extreme Points

Example 5 Find if possible Implicit Differentiation Properties of Definite Integrals Local Extreme Points

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. Implicit Differentiation Properties of Definite Integrals Local Extreme Points