`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

Answer

7

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