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(-00, -6] (-6, 4) 7) Define H(t) by H(t) = 2 -2 [4, 00) Calculate 1, H(t) dt Calculate , H(t) dt 3.

(-00, -6] (-6, 4) 7) Define H(t) by H(t) = 2 -2 [4, 00) Calculate 1, H(t) dt Calculate , H(t) dt 3.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 7: Piecewise Function and Integrals** Define \( H(t) \) by the piecewise function: \[ H(t) = \begin{cases} 3 & \text{for } t \in (-\infty, -6] \\ -\frac{t}{2} & \text{for } t \in (-6, 4) \\ -2 & \text{for } t \in [4, \infty) \end{cases} \] ### Tasks: **Calculate the following integrals:** 1. \(\int_{-10}^{0} H(t) \, dt\) 2. \(\int_{-1}^{1} H(t) \, dt\) 3. \(\int_{10}^{15} H(t) \, dt\)
Transcribed Image Text:**Problem 7: Piecewise Function and Integrals** Define \( H(t) \) by the piecewise function: \[ H(t) = \begin{cases} 3 & \text{for } t \in (-\infty, -6] \\ -\frac{t}{2} & \text{for } t \in (-6, 4) \\ -2 & \text{for } t \in [4, \infty) \end{cases} \] ### Tasks: **Calculate the following integrals:** 1. \(\int_{-10}^{0} H(t) \, dt\) 2. \(\int_{-1}^{1} H(t) \, dt\) 3. \(\int_{10}^{15} H(t) \, dt\)
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