In the following exercises, evaluate the triple integrals over the bounded region \(E=\left\{(x, y, z) \mid a \leq x \leq b, h_{1}(x) \leq y \leq h_{2}(x), e \leq z \leq f\right\}\).

\(\iiint_{E}(y \ln x+z) d V\), where \(E=\{(x, y, z) \mid 1 \leq x \leq e, 0 \leq y \leq \ln x, 0 \leq z \leq 1\}\)

Text Transcription:

E=\left\{(x, y, z) \mid a \leq x \leq b, h_{1}(x) \leq y \leq h_{2}(x), e \leq z \leq f\right\}

\iiint_{E}(y \ln x+z) dV

E=\{(x, y, z) \mid 1 \leq x \leq e, 0 \leq y \leq \ln x, 0 \leq z \leq 1\}

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