Solve this sample test

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timer Asked: Apr 15th, 2018

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Please solve this sample test with all the steps clear and precise. It is important for studying to the test.

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MAC2283 Engineering Calculus III Spring 2018 Sample Test 3 No calculating device will be allowed for the exam 3. ZZ y 2 dA, where R is the triangular region with vertices (0, 0), (1, 1), and 1. Evaluate R (1, 0). 2. Find the volume of the solid that lies under the plane z = x + y and above the region R in the xy-plane bounded by the line y = 2x and the parabola y = x2 . 3. Find the volume of the solid in the fist octant that is bounded by the planes x + y + z = 1, x − y = 0 2x − y = 0. Z 1 1 Z 4. Evaluate 0 Z √ x2 + 1 dx dy. y 0 √ Z 4−x2 cos(x2 + y 2 ) dy dx. 5. Evaluate −2 Z 0 √ 1/ 2 Z 6. Evaluate 0 0 x 1 Z p dy dx + x2 + y 2 1 √ 1/ 2 √ Z 0 1−x2 1 p dy dx. 2 x + y2 7. Find the volume of the solid in the first octant bounded by cylinder z = 1 − x2 and the plane x + y = 1. ZZZ 1 2 2 2 p 8. Find ex +y +z dV, where R is the solid in the fist octant enx2 + y 2 + z 2 R closed by the sphere x2 + y 2 + z 2 = 1. ZZZ 9. Find x dV, where R is the solid in the fist octant which lies inside the cone p R z = x2 + y 2 and the sphere x2 + y 2 + z 2 = 1. ZZ 7y 1 10. Find e2− x+3y dA, where R is the domain bounded by the lines 2x−y = 0, R x + 3y 2x − y = 1, x + 3y = 0, and x + 3y = 2. 1
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