QQuestion
Question
Tính ∭E^6z^2dV với E là khối bên dưới mặt phẳng 8x+ 2y+z= 20 và trong phần tám thứ nhất của hệ trục Oxy.
Chú ý kết quả điền vào là số thập phân làm tròn đến 3 chữ số sau dấu phẩy.
11 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:This problem is asking for the triple integral of the function Loading... over the region E, which is below the plane defined by the equation Loading... and in the first octant of the coordinate system (meaning x, y, and z are all non-negative).
Loading...
over the region E, which is below the plane defined by the equation Loading...
and in the first octant of the coordinate system (meaning x, y, and z are all non-negative).Step 2:: Identify the limits of integration
Loading...
The plane
Loading...
gives us the upper limit for z.Step 3:: Set up the triple integral
Loading...
The triple integral of a function over a region E is given by: So the triple integral becomes:
Final Answer
The exact numerical value of the triple integral will depend on the method used to evaluate it. The problem asks for the answer to be rounded to three decimal places. Without knowing the exact numerical method used, it's not possible to provide a specific answer. However, the process outlined above is the correct approach to setting up and beginning to solve the problem.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students
Related Questions
No related questions found