Chapter 5.4, Problem 66E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Suppose that a volcano is erupting and readings of the rate *r*(*t*) at which solid materials are spewed into the atmosphere are given in the table. The time *t* is measured in seconds and the units for *r*(*t*) are tonnes (metric tons) per second.

(a) Give upper and lower estimates for the total quantity *Q*(6) of erupted materials after six seconds.

(b) Use the Midpoint Rule to estimate *Q*(6).

(a)

To determine

**To find:** The total quantity of upper and lower estimates of erupted materials after six seconds duration.

Explanation

**Given information:**

The region lies between

**Calculation:**

The expression to find the upper estimate for total quantity of erupted materials

Here, the rate of volcanic eruption at time

Substitute 6 for *n* in Equation (1).

Substitute

Therefore, the upper estimate for total quantity of erupted materials is

(b)

To determine

**To find:** The total quantity of erupted materials using Midpoint Rule.

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