   Chapter 5.3, Problem 51E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.y = sin x, 0 ≤ x ≤ π

To determine

The area under the curve y=sinx.

Explanation

Given information:

The equation of curve is y=sinx (1)

The region lies between x=0 and x=π.

Calculation:

Find y value using the curve function:

Substitute 0 for x in Equation (1).

y=sinx=sin0y=0

Hence, the co-ordinates (x,y) is (0,0).

Substitute 1 for x in Equation (1).

y=sinx=sin45y=0.850

Hence, the co-ordinates (x,y) is (1,0.850).

Similarly calculate for remaining y values and tabulate the results as in Table (1).

 x y 0 0.00 45 0.85 90 0.89 180 0.00

Draw the diagram for the curve function y=sinx using the calculated values in Table (1).

Show the diagram for the curve function y=sinx as in Figure (1)

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