08 - ApproxInt - Ex Approximate sin e x 1 2 ± dx n = 6 x...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Trapezoid Rule We have used a left and right Riemann sum to approximate an integral. Now we will introduce two more methods of approximation – the Trapezoid Rule and Simpson’s Rule. Trapezoid Rule: Instead of rectangles, we will use trapezoids to approximate the area.
Image of page 1

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

View Full Document Right Arrow Icon
The Trapezoid Approximation = LRS+RRS 2 Ex. Approximate sin e x ) 1 2 dx , n = 5 x f(x)
Image of page 2
Ex. Approximate x dx 1 4 , n = 3 Simpson’s Rule: Use parabolas to estimate the area. For parabolas, we must use two intervals so n will always be even.
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Ex. Approximate sin e x 1 2 ± dx , n = 6 x f(x) Ex. Approximate x ± dx 1 4 , n = 4 Do: 1 Find the trapezoid rule approximation to f ( x )± dx-3 , using the following table of values. x-3-2.5-2-1.5-1-.5 f(x) 2 1 1 1 2 3 2. Find the Simpson’s rule approximation to the integral for the function on the given interval, using the same table of values. 3. Set up a Simpson’s rule approximation for x x ± dx ,± n 4 3 9 . Do not evaluate....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern