Subjects and resources that you bookmark will appear here.

1 min read•june 8, 2020

Anusha Tekumulla

This topic is similar to topic 8.9 except we will be **revolving our shape around other axes instead of just the x- or y-axis.** This can get a bit confusing but we’ll simplify it for you with an example problem.

To keep it simple, we’ll use the same y = √x curve from the example in topic 8.9. This time, however, we’ll revolve around the line y = 1 from x = 1 and x = 4.

If you **rotate** this region around the line y = 1, the cross sections will be circles with radii (√x) - 1. This is because our region is now shifted up one. When revolving around a line that is not the x- or y-axis, we must remember to take that into account when calculating the radius of our discs. With that, the area of each cross section will be π((√x) - 1)2. This can be **simplified **to π(x - 2√x + 1). Now we can **integrate **π(x - 2√x + 1) from x = 1 and x = 4 to get the volume.

Thousands of students are studying with us for the AP Calculus AB/BC exam.

join nowBrowse Study Guides By Unit

✍️

Free Response Questions (FRQ)

🧐

Multiple Choice Questions (MCQ)

♾

Unit 10: Infinite Sequences and Series (BC Only)

👑

Unit 1: Limits & Continuity

🤓

Unit 2: Differentiation: Definition & Fundamental Properties

🤙🏽

Unit 3: Differentiation: Composite, Implicit & Inverse Functions

👀

Unit 4: Contextual Applications of the Differentiation

✨

Unit 5: Analytical Applications of Differentiation

🔥

Unit 6: Integration and Accumulation of Change

💎

Unit 7: Differential Equations

🐶

Unit 8: Applications of Integration

🦖

Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)