Evaluate the integrals by changing the order of integration in an appropriate way.
int_(0)^(4)int_(0)^(1)int_(2y)^(2)(4cos (x^(2)))/(2sqrt(z))dx dy dz

1 Answers

Best Answer

Change the order of integration from dxdydz to dydxdz.
Now we have:
int_(0)^(4)int_(0)^(1)int_(2y)^(2)(4cos (x^(2)))/(2sqrt(z))dx dy dz=int_(0)^(4)int_(0)^(2)int_(0)^((1)/(2)x)(4cos x^(2))/(2sqrt(z))dy dx dz
=int_(0)^(4)int_(0)^(2)(4cos x^(2))/(2sqrt(z))(x)/(2)dx dz=int_(0)^(4)int_(0)^(2)(xcos x^(2))/(sqrt(z))dx dz
=int_(0)^(4)[(sin x^(2))/(2sqrt(z))]_(x=0)^(x=2)dz
=sin 4[sqrt(z)]_(z=0)^(z=4)
=2sin 4
Result:
2sin 4