Change Of Variables - Numericals
Hint:
Change Of Variables - Numericals
𝑥
3 2(1−3)
1. Switch the integration order in 𝐼 = ∫0 ∫
𝑓 (x,y)dydx.
𝑥2
√
−2 1− 2
3
2. Evaluate integral ∬𝑅 𝑥 dA where R is the region enclosed by y =
√𝑥, y= 6 – x, and y = 0.
3. Use double integration to find the volume of the solid enclosed
by the cylinder 4𝑥 2 + 𝑦 2 = 9 by the
planes 𝑧 = 0 and 𝑧 = 𝑦 +
4.
4. ) Calculate ∬ 𝑟 3 𝑑𝑟𝑑𝜃over the area included
between
𝑟 = 2𝑠𝑖𝑛𝜃𝑎𝑛𝑑𝑟 = 4 𝑠𝑖𝑛𝜃.
3
5. Calculate ∬ 𝑟 𝑑𝑟𝑑𝜃over the area included between
𝑟 = 2 𝑐𝑜𝑠𝜃𝑎𝑛𝑑𝑟 = 4 𝑐𝑜𝑠𝜃.