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Chapter 13: Problem 4

Consider the integral \(\int_{1}^{3} \int_{-1}^{1}\left(2 y^{2}+x y\right) d y d x .\) State the variable of integration in the first (inner) integral and the limits of integration. State the variable of integration in the second (outer) integral and the limits of integration.

Short Answer

Expert verified
Answer: For the inner integral, the variable of integration is y with limits -1 to 1. For the outer integral, the variable of integration is x with limits 1 to 3.

Step by step solution

01

Inner integral variable and limits

The inner integral is given as \(\int_{-1}^{1}\left(2 y^{2}+x y\right) d y\). Here, the variable of integration is \(y\), and the limits are from \(-1\) to \(1\).
02

Outer integral variable and limits

The outer integral is given as \(\int_{1}^{3} \left(\text{Inner Integral result}\right) d x\). Here, the variable of integration is \(x\), and the limits are from \(1\) to \(3\).

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