# Chapter 15: Multiple Integrals - Section 15.5 - Triple Integrals in Rectangular Coordinates - Exercises 15.5 - Page 902: 43

4

#### Work Step by Step

$\int^1_0 \int^1_{}\sqrt[3] z \int^{\ln3}_0 \frac{\pi e^{2x}sin(\pi y^2)}{y^2}$ dx dy dz =$\int^1_0 \int^1_{\sqrt[3] z} \frac{4 \pi sin (\pi y^2)}{y^2}$ dy dz =$\int^1_0 \int^{y^3}_0 \frac{4\pi sin(\pi y^2)}{y^2}$ dz dy =$\int^1_0 4\pi y sin(\pi y^2)dy$ =$[-2cos(\pi y^2)]^1_0$ =$-2(-1)+2$ =4

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