{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# n7_2 - Section 7.2 Volume courtesy Chia-Rong Chen 1 A...

This preview shows pages 1–3. Sign up to view the full content.

Section 7.2 Volume courtesy: Chia-Rong Chen 1. A cylinder has a contant cross section. Its volume is V = Ah where A = area of the base, and h = height. 2. For a solid S with nonuniform cross-sectional area, we use the slicing method : Cut a thin slice perpendicular to the x -axis at x with a thickness dx and a cross-sectional area A ( x ). The approximate volume of this thin slice is then A ( x ) dx . Adding the volumes of all the thin slices and taking the limit of the Riemann sums, we obtain the volume of S as a definite integtal: V = lim bardbl P bardbl→ 0 n summationdisplay i =1 A ( x i x i = integraldisplay b a A ( x ) dx eg.(1) A solid has a right triangular base of 6 units along the x -axis and 2 units along the y -axis. Its cross sections perpendicular to the x -axis are semi-circles. Find its volume. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
eg.(2) Find the volume of the solid whose base is the region bounded by the parabola y = x 2 and y = 4. The cross sections perpendicular to the y -axis are equilateral triangles.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern