Suppose `y=f(x)` and `y=g(x)` are two continuous functiond whose graphs intersect at the three points `(0,4),(2,2)` and `(4,0)` with `f(x) gt g(x)` for ` 0 lt x lt 2` and `f(x) lt g(x)` for `2 lt x lt 4`. If `int_0^4[f(x)-g(x)]dx=10 and int_2^4[g(x)-f(x)]dx=5` the area between two curves for `0 lt x lt 2`,is (A) 5 (B) 10 (C) 15 (D) 20

Options

A. 5
B. 10
C. 15
D. 20

Answer

C

Explanation

Given `int_(0)^(4)f(x)dx-int_(0)^(4)g(x)dx=10`

`therefore" "(A_(1)+A_(3)+A_(4))-(A_(2)+A_(3)+A_(4))=10`
`therefore" "A_(1)-A_(2)=10" (i)"`
Also `int_(2)^(4)g(x)dx-int_(2)^(4)f(x)Dx=5`
`(A_(2)+A_(4))-A_(4)=5`
`therefore" Adding (i) and (ii), A"_(1)=15`