Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

The base of s is the region enclosed by the parabola y = 3 − 2x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.

Sagot :

The volume of the base of the region enclosed by the parabola is; V = 9

Integral Volume of a Solid

The length of each cross-section is determined by the horizontal distance (parallel to the x-axis) from one end of the parabola to the other.

Thus;

y = 3 - 2x²

Making x the subject gives us;

x = ±√[(3 - y)/2]

Thus;

The horizontal distance is;

√[(3 - y)/2] - (-√[(3 - y)/2])

⇒ 2√[(3 - y)/2]

The area of each cross-section is simply the square of the section's side length, so the area would be;

A = (2√[(3 - y)/2])²

A = 6 - 2y

Thus, volume is;

V = [tex]\int\limits^3_0 {6 - 2y} \, dy[/tex]

Solving this gives V = 9

Read more about integral volume of solids at; https://brainly.com/question/14845570

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.