💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# The given curve is rotated about the y-axis. Find the area of the resulting surface.$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 1$ , $0 \le y \le 1$

## $$\frac{6}{5} \pi$$

#### Topics

Applications of Integration

### Discussion

You must be signed in to discuss.
##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp

### Video Transcript

this question asked us to use the bounds of 01 and find the area of the resulting surface. Given the fact that the curve is retained about the Y axis. What we know is we're looking from 0 to 1 is our two bounds and then we have two pi. We have the original expression and then we have this multiplied by the square root of one plus one minus y two. The 2/3 over Why the 2/3 do you? Why, We know he could write this out as to pie times the integral from 0 to 1. The reason why two pies on the outside is because estate in the textbook, because it is a constant, it doesn't need to be integrated. It could just be pulled out and then be multiplied by what's in the end. Okay, What we know we now have is U substitution if you is one minus one of the 2/3 member usually used u substitution with what's in parentheses. As you can see over here, do you is negative 2/3 wide to the negative 1/3 d Y. This now means that we have negative 6/5 spy times and then our upper minus or lower bound. This is equivalent to six over five pi the negative negative cancer.

#### Topics

Applications of Integration

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp