`f(x)` is a continuous function for all real values of `x` and satisfies `int_n^(n+1)f(x)dx=(n^2)/2AAn in Idot` Then `int_(-3)^5f(|x|)dx` is equal to (a) `(19)/2` (b) `(35)/2` (c) `(17)/2` (d) none of these

Options

A. `19//2`
B. `35//2`
C. `17//2`
D. none of these

Answer

B

Explanation

`int_(-3)^(5)f(|x|)dx=int_(-3)^(3)f(|x|)dx+int_(3)^(5)f(|x|)dx`
`=2int_(0)^(3)f(x)dx+int_(3)^(5)f(x)dx`
`=2(int_(0)^(1)f(x)dx+int_(1)^(2)f(x)dx+int_(2)^(3)f(x)dx)`
`+(int_(3)^(4)f(x)dx+int_(4)^(5)f(x)dx)`
`=2(0+1/2+(2^(2))/2)+(9/2+16/2)=35/2`