If `int_a^b|sinx|dx=8` and `int_0^(a+b)|cosx| dx=9` , then find the value of `int_a^b xsinx dx`.

Options

A. `a+b=(9pi)/2`
B. `|a=b|=4pi`
C. `a/b=15`
D. `int_(a)^(b)sec^(2)xdx=0`

Answer

A, B

Explanation

We know `int_(a)^(b)|sinx|dx` represents the area under the curve from `x=a` to `x=b`.We also know that area from `x=a` to `x=a+pi` is 2.
`:. int_(a)^(b)|sinx|dx=8` or `b-a=(8pi)/2`……………1
Similarly, `int_(0)^(a+b)|cosx|dx=9` or `a+b-0=(9pi)/2`................2
fro 1 and 2 `a=(pi)/4` and `b=(17pi)/4`
`:.|a+b|=(9pi)/2,|a-b|-4a/b=17`
Obviously, `int_(a)^(b)sec^(2)xdx!=0`