CK-12-Calculus

4.8. Numerical Integration http://www.ck12.org

2. We estimated errors for the Trapezoidal Rule.


3. We used Simpson’s Rule to solve problems.


4. We estimated Errors for Simpson’s Rule.

Multimedia Links

For video presentations of Simpson’s Rule(21.0), see Simpson’s Rule, Approximate Integration (7:21)

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/566

and Math Video Tutorials by James Sousa, Simpson’s Rule of Numerical Integration (8:48).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/567

Review Questions

1. Use the Trapezoidal Rule to approximate∫ 01 x^2 e−xdxwithn= 8.


2. Use the Trapezoidal Rule to approximate∫ 14 ln√xdxwithn= 6.


3. Use the Trapezoidal Rule to approximate∫ 01

√

1 +x^4 dxwithn= 4.

4. 
   

   Use the Trapezoidal Rule to approximate∫ (^131) xdxwithn= 8.

   
   


5. 
   

   How large should you takenso that the Trapezoidal Estimate for∫ 131 xdxis accurate to within 0.001?

   
   


6. 
   

   Use Simpson’s Rule to approximate∫ 01 x^2 e−xdxwithn= 8.

   
   


7. 
   

   Use Simpson’s Rule to approximate∫ 14 √xlnxdxwithn= 6.

   
   


8. 
   

   Use Simpson’s Rule to approximate∫ 02 √x (^41) + 1 dxwithn= 6.

   
   


9. 
   

   Use Simpson’s Rule to approximate∫ 01

   
   

√

1 +x^4 dxwithn= 4.

10. How large should you takenso that the Simpson Estimate for∫ 02 edxis accurate to within 0.00001?

Texas Instruments Resources

In the CK-12 Texas Instruments Calculus FlexBook® resource, there are graphing calculator activities designed
to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9729.