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Question

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

A
20
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B
15
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C
10
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D
5
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Solution

The correct option is B 15
Given: y=f(x) and y=g(x) intersect at (0,4),(2,2),(4,0)
f(x)>g(x) for x(0,2)
f(x)<g(x) for x(2,4)

Inferences: f(0)=g(0)=4; f(2)=g(2)=2
f(4)=g(4)=0

Area =20(f(x)g(x))dx

Given 40(f(x)g(x))dx=10
20(f(x)g(x))dx+42(f(x)g(x))dx=10
20(f(x)g(x))dx42(g(x)f(x))dx=10
20(f(x)g(x))dx=10+5=15 sq. units

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