You are here:

Calculus/AP Calculus

Advertisement

Expert: - 4/14/2008


Question
My teacher assigned this question in our homework over the weekend and I want to know if I'm on the right track.

The base of a solid S is the shaded region in the first quadrant enclosed by the coordinate axes and the graph of y = square root (1-sinx). For each x, the cross section of S perpendicular to the x - axis at the point (x,0) is an isosceles right triangle whse hypotenuse lies in the xy-plane.
A) Find the area of the triangle as a function of x.
B) Find the volume of S.

Answer
The length of the hypoteneuse is y and the two legs are then
y/root(2).  The area of each of these triangles is the product of the two sides / 2.

The endpoints are where sin(x)=1.

Determine the endpoints, find the function for the area at each point, then integrate between them.

When finding the area at each point, the squareroot will disappear.

Hope you can figure it out from here, but if not, ask me more questions on the subject.

Happy studying!

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.