Calculus and AnalysisEvaluate the integrals by changing the order of integration in an appropriate way.
2 months ago
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
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brothersosborneticketscalgary Staff answered 2 months ago
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
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