Problem

The given curve is rotated about the y-axis. Find…

01:26

Problem 17 Hard Difficulty

The given curve is rotated about the y-axis. Find the area of the resulting surface.

$ x = \sqrt{a^2 - y^2} $ , $ 0 \le y \le \frac{a}{2} $

Answer

$$
\pi a^{2}
$$

Topics

Applications of Integration

Calculus: Early Transcendentals

Chapter 8

Further Applications of Integration

Section 2

Area of a Surface of Revolution

Discussion

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Video Transcript

we know the first thing you can do is we can find the derivative of X with respect a Y. In other words, we can write negative Why over square root of any squared minus y square Again, we writing this in terms of why Which means now when we plugged into our and to grow we have the bounds from zero to a over to and we have square root of a squared minus four I squared, which we have over here times a squared over a squared minus wife's word. Do you? Why? And this was from the original problem. This part which means this simplifies to two pi times integral from zero over to squirt of a squared, which is just a the other stuff cancels out the skirt and squared, cancels out this simple fires taking the intro a of why, from zero to a divided by two, it's at the point. Now we can plug in to pi eight times over to minus zero. Is pi a square

Amrita B.