Practice Integration Involving Delta Function (12.4.5) - Dirac Delta Function

Practice: Integration Involving Delta Function

Lesson 12.4.5Dirac Delta Function

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8 questions

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6 sample questions

Question 1.
What is the value of $\int_{-1}^{1} \delta(x) dx$ ?
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Recall that the integral of the delta function over its entire range is one.
Question 2.
If $c$ is outside the limits $a$ and $b$ , what does $\int_a^b f(x) \delta(x-c) dx$ equal?
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Think about how the sifting property works here.
3Question 3.
What is the integral of the delta function over its entire domain?
- 0
- 1
- ∞
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Remember the property of the delta function.
4Question 4.
True or False: The Dirac delta function has non-zero values everywhere.
- True
- False
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Think about its definition.
Question 5.
Evaluate the integral $\int_{-2}^{2} 3 \delta(x-1) dx$ . What is the result and why?
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Use the sifting property for this calculation.
Question 6.
Discuss the implications of modeling an instantaneous load on a beam using the Dirac delta function. How does this simplify our calculations?
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Think through how such conditions would change typical load evaluations.

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