Unit 06 Core Practice

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Core pathway

Advanced Applications of Integration

College-level fluency, interpretation, and verification.

1. Find the area between y=x and y=x² on [0,1].

2. Which statement best describes the central reasoning in Area Between Curves & Intersection Analysis?

3. A solid has square cross-sections perpendicular to x-axis over 0≤x≤2 with side x. Find V.

4. Which statement best describes the central reasoning in Volumes by General Slicing?

5. Rotate y=√x, 0≤x≤4, about the x-axis.

6. Which statement best describes the central reasoning in Disks & Washers?

7. Rotate y=x², 0≤x≤1, about the y-axis.

8. Which statement best describes the central reasoning in Cylindrical Shells?

9. Find the length of y=(2/3)x^{3/2} from 0 to 1.

10. Which statement best describes the central reasoning in Arc Length?

11. Rotate y=x, 0≤x≤1, about the x-axis.

12. Which statement best describes the central reasoning in Surface Area of Revolution?

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