Question

(a) Use the Trapezoidal rule with 4 equal partitions to approximate ? integral (from -1 to...

(a) Use the Trapezoidal rule with 4 equal partitions to approximate

?
integral (from -1 to 1) (x^2 +1)dx

via the formula Tn =(∆x/2)(y0+2y1+...+2yn−1+yn )with n=4, and ∆x=(b−a)/n

(b) Compare the actual error, found by direct integration minus the approximation, with the known error bound for the Trapezoidal rule

|ETn| ≤ (f′′(c)/12n^2) (b−a)^3, 12n2

where c is a point at which the absolute value of the second derivative is maximized.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

(a) Use the Trapezoidal rule with 4 equal partitions to approximate

?
integral (from -1 to 1) (x^2 +1)dx

via the formula Tn =(∆x/2)(y0+2y1+...+2yn−1+yn )with n=4, and ∆x=(b−a)/n

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use the trapezoidal rule with n = 4 to approximate the integral with a upper bound...
Use the trapezoidal rule with n = 4 to approximate the integral with a upper bound of (1/3) and a Lower bound of 0 1/3 ∫ √ (1- 9x^2 )dx ******* by the way square root covers 1- 9x^2 in the integral fully for the entire equation b. ) Use Simpson’s rule with n = 4 to approximate the same integral.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with...
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 4 0 ln(5 + ex) dx, n = 8 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule
Use the trapezoidal rule with n=4 steps to estimate the integral.   Integral from -1 to 1(x^2+6)dx...
Use the trapezoidal rule with n=4 steps to estimate the integral.   Integral from -1 to 1(x^2+6)dx (-1 is on the bottom)  
Use the Trapezoidal Rule to approximate 4 on top ∫ on bottom 2 (9x^2+1) dx using...
Use the Trapezoidal Rule to approximate 4 on top ∫ on bottom 2 (9x^2+1) dx using n=4. Round your answer to the nearest tenth. Evaluate the exact value of ∫42(9x2+1) dx and compare the results. Trapezoidal Approximation ≈ Exact Value=
Use the Midpoint Rule with n = 4 to approximate the integral from 1 to 3...
Use the Midpoint Rule with n = 4 to approximate the integral from 1 to 3 of 1/x dx.
Use the trapezoidal rule with 4 rectangles to estimate the integral of ex^2 dx from 1...
Use the trapezoidal rule with 4 rectangles to estimate the integral of ex^2 dx from 1 to 3
Find M of the following integration and find the relation error use the trapezoidal rule to...
Find M of the following integration and find the relation error use the trapezoidal rule to approximate the definite integral. Use n=4
Use the Trapezoidal Rule to approximate 8 on top ∫ on the bottom 5 ln(x^2+4) dx...
Use the Trapezoidal Rule to approximate 8 on top ∫ on the bottom 5 ln(x^2+4) dx using n=3. Round your answer to the nearest hundredth.
Estimate the minimum number of subintervals to approximate the value of Integral from negative 2 to...
Estimate the minimum number of subintervals to approximate the value of Integral from negative 2 to 2 left parenthesis 4 x squared plus 6 right parenthesis dx with an error of magnitude less than 4 times 10 Superscript negative 4 using a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for​ Simpson's Rule.
Estimate the minimum number of subintervals needed to approximate the integral integral subscript 0 superscript 4...
Estimate the minimum number of subintervals needed to approximate the integral integral subscript 0 superscript 4 open parentheses 7 x squared minus 4 x close parentheses d x with an error of magnitude less than 10-4 using Simpson's Rule. Error Estimates in the Simpson's Rule: If f(4) is continuous and M is any upper bound for the values of |f(4)| on [a, b], then the error ES in the Simpson's Rule approximation of the integral of f from a to...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT