The Double Integral over more General Regions Questions, guaranteed and verified 100%

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The Double Integral over more General Regions- HW Problems


Sketch the region over which the integral is being taken and then
evaluate the integral.
1 𝑥
1. ∫0 ∫0 (𝑥 + 𝑦)𝑑𝑦𝑑𝑥
2 4−𝑥 2 2
2. ∫0 ∫0 (𝑥 + 1)𝑑𝑦𝑑𝑥
1 𝑥
3. ∫0 ∫𝑥 2(2𝑦)𝑑𝑦𝑑𝑥
2 1+𝑦 2
4. ∫0 ∫0 (2𝑥 − 2𝑦)𝑑𝑥𝑑𝑦


Evaluate the following integrals.

5. ∬𝐷 sin(𝑦) 𝑑𝐴, Where 𝐷 is the region bounded by 𝑦 = 3𝑥, 𝑦 = 𝑥,
𝜋 𝜋
𝑥= , 𝑥= (Always start by drawing the region 𝐷)
6 4

6. ∬𝐷 (𝑥𝑦)𝑑𝐴, Where 𝐷 is the region bounded by 𝑦 = 𝑥 2 − 10 and
𝑦 = −𝑥 2 + 8.


7. Find the volume bounded by 𝑧 = 25 − 𝑥 2 − 𝑦 2 and the four planes
𝑧 = 0, 𝑦 = 0, 𝑦 = 𝑥, and 𝑥 + 𝑦 = 2.


8. Find the area of a circle of radius 3 using a double integral.


9. Find the area of the triangle with vertices at (−2, 0), (2, 0), and
(0,4) using a double integral.