Step by Step Solutions

[Solution] (a) Change the order of integration in the following integrals: i ∫_0^2 ∫_1^e^x d y d x ii. ∫_-1^1 ∫_-√1-x^2^√1-x^2

Question: (a) Change the order of integration in the following integrals:

\(\mathrm{i}\)

\[\int_{0}^{2} \int_{1}^{e^{x}} d y d x\]

ii.

\[\int_{-1}^{1} \int_{-\sqrt{1-x^{2}}}^{\sqrt{1-x^{2}}} y d y d x\]

(b) Evaluate the integral

\[\int_{R}(x+y) \mathrm{d} d x d y\]

where \(R\) is the triangular region bounded by the lines \(y=2 x, y=\frac{x}{2}\) and \(y=3-x\).

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