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![**Evaluate**
\[ \int_{x=0}^{1} \int_{y=x}^{1} xe^{y^3} \, dy \, dx \]
This expression is a double integral. The task is to evaluate the integral of the function \(xe^{y^3}\), with respect to \(y\) and \(x\). The order of integration is from \(y = x\) to \(y = 1\), and from \(x = 0\) to \(x = 1\). The inner integral is with respect to \(y\), while the outer integral is with respect to \(x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81e8ba16-e7f4-4cb8-bc35-ac7ab5472c5c%2F21fe05ca-9fc2-42aa-887d-b818d7b5d0b2%2Fox3xr3n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate**
\[ \int_{x=0}^{1} \int_{y=x}^{1} xe^{y^3} \, dy \, dx \]
This expression is a double integral. The task is to evaluate the integral of the function \(xe^{y^3}\), with respect to \(y\) and \(x\). The order of integration is from \(y = x\) to \(y = 1\), and from \(x = 0\) to \(x = 1\). The inner integral is with respect to \(y\), while the outer integral is with respect to \(x\).
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