`L e tJ=int_(-5)^(-4)(3-x^2)tan(3-x^2)dx and K=int_(-2)^(-1)(6-6x+x^2)` `tan(6x-x^2-6)dxdot` Then (J+K) equals _____

Answer

0

Explanation

We have `J=int_(-5)^(-4)(3-x^(2))tan(3-x^(2))dx`
Put `(x+5)=t`. Then
`J=int_(0)^(1)(3-(t-5)^(2))tan(3-(t-5)^(2))dt`
`=int_(0)^(1)(-22+10t-t^(2))tan(-22+10t-t^(2))dt`
Now `K=int_(-2)^(-1)(6-6x+x^(2))tan(6x-x^(2)-6)dx`
Put `(x+2)=z`. Then
`K=int_(0)^(1)(6-6(z-2)+(z-2)^(2))tan(6(z-2)-(z-2)^(2)-6)`
`=int_(0)^()(22-10z+z^(2))tan(-22+10z-z^(2))dz`
Hence `(J+K)=0`