Posted by **anonymous** on Wednesday, January 30, 2008 at 9:58pm.

Let f(x) be the function e^sin(x/10). If you wanted to estimate the area under the curve for this function from 3 to 5, how many intervals would you need to use to be sure that your upper and lower bounds differered by no more than .01?

- CALC -
**drwls**, Wednesday, January 30, 2008 at 11:17pm
That is a slowly varying function over that interval. It increases from 1.3438 at x=3 to 1.6151 at x = 5. An approximate value for the integral is the mean value times 2, or 2.96.

I suggest you review and apply Simpson's Rule for numerical integration and use it with ten intervals (h = 0.2). There is a description of the method and a formula for its accuracy at

http://mathworld.wolfram.com/SimpsonsRule.html

If you get about the same value with four intervals as you get with ten, you can be quite sure the error will be comparable to the difference betrween the two calculations.

Using Simpson's Rule with four intervals, I get 2.9378 for the integral.

## Answer this Question

## Related Questions

- Python programming - A standard problem in mathematics is to measure the area ...
- CALC - area under a curve - You have an unknown function that is monotone ...
- math-calc - for x (-12, 10) the function f is defined: f(x)=x^7(x+2)^2 On which ...
- I would like to understand my calc homework:/ - Consider the differential ...
- Calc 1 - Use a graph to give a rough estimate of the area of the region that ...
- Calc. - Find the area of the region bounded by the parabola y=x^2, the tangent ...
- Calculus - Use a simple area formula from geometry to find the area under ...
- trig - use the function G(x)=x^3-8x +1 b) identify and verify the y intercept of...
- AP Stats - I generally know how to use the normalcdf function on my calculator, ...
- Calc 121 - Okay, how would you go about finding the area of a curve from 1 to 4...

More Related Questions