Chapter 5.1, Problem 4E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

(a) Estimate the area under the graph of *f*(*x*) = sin *x* from *x* = 0 to *x* = *π*/2 using four approximating rectangles and right endpoints. Sketch the graph and the rectangles. Is your estimate an underestimate or an overestimate?

(b) Repeat part (a) using left endpoints.

**(a)**

To determine

**To Analyze:**

Whether the estimate is an underestimate or an overestimate using right endpoints.

Explanation

**Given information:**

The curve function is

The region lies between

The number of rectangles

Draw the graph for the function

Draw four approximating rectangles using right end points for the function

The expression to find the lower estimate of areas of *n* rectangles

Here, the right endpoint height of the first rectangle is *n*^{th} rectangle is

Find the width

Here, the upper limit is *b*, the lower limit is *a*, and the number of rectangles is *n*.

Substitute *b*, 0 for *a*, and 4 for *n* in Equation (2)

(b)

To determine

**To Analyze:**

Whether the estimate is an underestimate or an overestimate using right endpoints.

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