Question
Asked Nov 19, 2019
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The graph off is shown. Evaluate each integral by interpreting it in terms of areas.
У
yf(x)
х
0
18
(a)
f(x) dx
(b)
f(x) dx
(c)
f(x) dx
15
(d)
f(x) dx
24
12
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The graph off is shown. Evaluate each integral by interpreting it in terms of areas. У yf(x) х 0 18 (a) f(x) dx (b) f(x) dx (c) f(x) dx 15 (d) f(x) dx 24 12

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Expert Answer

Step 1

By integration with respect to x axis it means that find area between the curve and x axis.

If curve is below the line, then integration result will be negative of area between curve and x axis.

(a) Evaluate the value of the given integral.

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6 This is the area between curve and x axis in the region x-0 to x-6 The area can be calculated using counting grids between graph and x axis in the region. The area comprises 3 full grid and 2 half grid so total of 4 grids.so area is 4. Thus, f(x)dx 4 0

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Step 2

(b) Evaluate the value of the given integral.

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15 Now we need to find area in the region x-0 to x-15. The area comprises of 7 full grid,2 half grid, and another two grid area from side.so total of 10 grid. So the area is 10.

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Step 3

(c) Evaluate the value of ...

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21 15 Now region is between x-15 and x-21 In this region area is below x axis, so integral will be negative of area. The area comprises of 1full grid and 2 grid from sides.so total of three. So area is 3, integral will be -3 21 Jf(xd3 15

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