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Question

If two functions f(x) and g(x) defined on R intersect each other at x = a & x =b then the area enclosed between these two functions will be -

A
ba[f(x)g(x)]dx
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B
ba[g(x)f(x)]dx
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C
ba[f(x)g(x)]|dx
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D
None of these
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Solution

The correct option is C ba[f(x)g(x)]|dx
We have seen that the area enclosed between f(x) and X- axis between x = a &
x = b can be given by baf(x)dx. Similarly the area between g(x) and X- axis between x = a &
x = b can be given by bag(x)dx.
Now if f(x)g(x)xϵ[a,b] then the area enclosed between f(x) and g(x) will be ba[f(x)g(x)]dx.

Similarly if g(x)f(x) then the area enclosed between f(x) and g(x) will be ba[g(x)f(x)]dx.
Thus the area enclosed depends on which function is greater. Therefore to be on safe side it’s better to take the absolute value.
So, the area enclosed will be ba|[f(x)g(x)]|dx

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