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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
BuyFindarrow_forward

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 = sec2x, 0 ≤ xπ/3

To determine

The area under the curve y=sec2x.

Explanation

Given information:

The equation of curve is y=sec2x (1)

The region lies between x=0 and x=π3

Find y value using the curve function.

Substitute 0 for x in Equation (1)

y=sec2x=sec2(0)=1

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

Substitute 1 for x in Equation (1).

y=x3=13y=1

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

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

xy
01.00
301.32
604.00

Draw the diagram for the curve function y=sec2x using the calculated values in Table (1).

Show the diagram for the curve function y=sec2x as in Figure (1).

Refer to Figure (1).

The shaded portion A1 represents area of rectangle and A2 represents area of triangle (approximation).

The area under the curve is calculated approximately by addition of A1 and A2

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