(Solved):   (30 points: 10 points each) Evaluate the integrals by changing to order of integration in ...

 

(30 points: 10 points each) Evaluate the integrals by changing to order of integration in an appropriate way. (a) \( \int_{0}^{4} \int_{0}^{1} \int_{2 y}^{2} \frac{4 \cos \left(x^{2}\right)}{2 \sqrt{z}} d x d y d z \) (b) \( \int_{0}^{1} \int_{0}^{1} \int_{x^{2}}^{1} 12 x z e^{2 x^{2}} d y d x d z \) (c) \( \int_{0}^{2} \int_{0}^{4-x^{2}} \int_{0}^{x} \frac{\sin 2 z}{4-z} d y d z d x \)