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9E: Chapter Review Exercises

Last updated

Nov 19, 2020
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- 9.7E: Exercises
- Mock Exams (Celebration of Learning)

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Exercise $\PageIndex{1}$

Sketch the regions and evaluate the integrals:

1) $\int_1^{\ln 8} \int_0^{\ln y} 2e^{x+y} \, dy dx$

2) $\int_0^{2} \int_x^{2} 3y^2 sin({xy}) \, dy dx$

3) $\int_0^{1} \int_0^{3} \frac{4x^2}{(y-1)^{2/3}} \, dy dx$

4) $\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \frac{3}{(x^2+1)(y^2+1)} \, dy dx$

5) $\int \int_{x^2+y^2 \leq 1} \ln (x^2+y^2)\, dA$

6) $\int_0^2 \int_{y/2}^1 y e^{x^3} \,dx dy$

7) $\int \int_Q \frac{dA}{(1+x^2)(1+y^2)}$ , where $Q$ is the first quadrant of the $xy-$ plane.

8) $\int \int_R x \cos (y) \,dA$ , where $R$ is the region bounded by the coordinate axes and the curve $y=1-x^2.$

Answer: Add texts here. Do not delete this text first.

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