💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here! # Find the exact area of the surface obtained by rotating the curve about the x-axis.$y = x^3$ , $0 \le x \le 2$

## $$S_{x}=\frac{\pi}{27}(145 \sqrt{145}-1)$$

#### Topics

Applications of Integration

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##### Top Calculus 2 / BC Educators   ##### Heather Z.

Oregon State University Lectures

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### Video Transcript

we know that we're gonna be using the formula the integral to pie from 0 to 2 times. Why, Diaz, which, in other words, essentially means we're gonna be having X cubed times square of one plus three x squared squared, which is nine X to the fourth D backs. Okay, now we know we can do some substitution. Over here you is one plus nine extra fourth, which means X cubed de acts is do you divide by 36? Which means we have two pi times integral from 1 to 1 45 you to the 1/2. Do you okay? Use the power method to integrate, which means increased the experiment by Juan divide by the new exponents. Now you're going to be plugging in our upper and are lower bounds. The lower bound plugged in. Just 2/3. You can see this is the upper ground plug. Done. This simplifies to pi over 27 times 1 45 times squared of 1 45 minus one #### Topics

Applications of Integration

##### Top Calculus 2 / BC Educators   ##### Heather Z.

Oregon State University Lectures

Join Bootcamp