QQuestion
Question
Tính ∭EzdV với E là khối nằm trong hình trụ z^2 +y^2 = 1 và ở giữa hai mặt phẳng x+ 1y+ 1z= 2,x= 0. Kết quả thu được là aπ
, tìm a
Chú ý kết quả điền vào là số thập phân làm tròn đến 3 chữ số sau dấu phẩy.
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Answer
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Step 1This problem is asking us to compute the triple integral of z over the region E, which is the volume inside the cylinder defined by the equation z^2 + y^2 = 1 and between the planes defined by the equations x + y + z = 2 and x = 0.
The result is given in the form of $$a\pi$$, and we need to find the value of a.
Step 2: Define the limits of integration
- For x: 0 to $$2 - (\cos\theta + \sin\theta)
First, we need to define the limits of integration. So, the limits of integration are: - For r: 0 to 1 - For θ: 0 to 2π
Final Answer
The value of a is 4 / 3, or approximately 1.333 when rounded to three decimal places.
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