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Question

Suppose y=f(x) and y=g(x) are two functions whose graphs intersect at three points (0,4),(2,2) and (4,0) with f(x)>g(x) for 0<x<2 and f(x)<g(x) for 2<x<4. if ∫40(f(x)−g(x))dx=10 and ∫42(g(x)−f(x))dx=5, the area between two curves for 0<x<2, is:

A
5
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B
10
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C
15
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D
20
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Solution

The correct option is D 15
f(x)>g(x) for 0<x<2 and f(x)<g(x) for 2<x<4.
if 40[f(x)g(x)]dx=10 and 42[g(x)f(x))]dx=5,
40[f(x)g(x)]dx=10
20f(x)g(x)dx+42f(x)g(x)dx=10
20(f(x)g(x))dx+42(g(x)f(x))dx=10
20(f(x)g(x))dx=15

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