Q.26 Your calculator should be able t... [FREE SOLUTION]

Chapter 4: Q.26 (page 340)

Your calculator should be able to approximate the area between a graph and the x-axis. Determine how to do this on your particular calculator, and then, in Exercises 21鈥�26, use the method to approximate the signed area between the graph of each function f and the x-axis on the given interval [a, b].
$f (x) = 1 - 2^{x}, [a, b] = [- 3, 1]$

Expert verified

Area between the function $f (x) = 1 - 2^{x}$ and x-axis on the interval [-3, 1] is $\frac{1}{8 \ln (2)} + 2 o r 2.18$ .

We have given function is $y = 1 - 2^{x}$ ,x- axis and the interval is [-3, 1].

Area between the curves is the area between a curve f(x) and a curve g(x) on an interval [a, b] given by,

$A = {鈭�}_{a}^{b} | f (x) - g (x) | d x$

We have $f (x) = 1 - 2^{x}$ , x-axis and the given interval is [-3, 1].

Area between the curve f(x) and x-axis is,

$A = {鈭�}_{- 3}^{1} | 1 - 2^{x} - 0 | d x$

= ${鈭�}_{- 3}^{0} 1 - 2^{x} d x + {鈭�}_{0}^{1} - 1 + 2^{x} d x$

localid="1648572228074" $= 3 - \frac{7}{8 \ln (2)} - 1 + \frac{1}{\ln (2)} = \frac{1}{8 \ln (2)} + 2 o r 2.18$

Hence, area between the curve $f (x) = 1 - 2^{x}$ and x-axis islocalid="1648572249321" $\frac{1}{8 \ln (2)} + 2 o r 2.18$ .

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