Question

In: Advanced Math

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specific value of n. (Round your answer to six decimal places).
∫₁³ sin (?) / ? ?? , ? = 4
Please show all work.

Expert Solution

Here we take the partition {1,(3/2),2,(5/2),3} of [1,3] to proceed.

Approximation by Trapezoidal Rule for n=4

By trapezoidal rule we have

Here

Where (The width of the sub-intervels)

Approximation by Mid-point rule for n=4

By mid point rule

Where are the mid points of the subintervel.
Here ,

where and

So,

Approximation by Simpson’s Rule for n=4

By simpson's rule,

Here

We were unable to transcribe this image

3. sin(t) -dt = T4 t (f(1)+253 +28(2) +2013) + f(3))

We were unable to transcribe this image

sin(t) -dt = T1 1 sin(1) 4 1 sin() + 2 + 2 JI sin(2) 2 sin) sin(3) + 2 + 3 t

0.034901

We were unable to transcribe this image

Colby Messinger answered 1 year ago

use the a) midpoint rule, b) Trapezoidal rule, and c) the Simpsons rule to approximate the...

use the a) midpoint rule, b) Trapezoidal rule, and c) the Simpsons rule to approximate the given integral with the value of n and round to 4 decimal places integral (from 0 to 1) e^-x^2 dx, n = 10 show work please

Explain and state the formula of (a) Trapezoidal rule, (b) the Midpoint Rule, and (c) Simpson’s...

Explain and state the formula of (a) Trapezoidal rule, (b) the Midpoint Rule, and (c) Simpson’s Rule and the error formula of each

Use the trapezoid rule, midpoint rule, and Simpson’s rule to approximate the given integrals with the...

Use the trapezoid rule, midpoint rule, and Simpson’s rule to approximate the given integrals with the given values of n. ?) ∫ ? ? / 1+? 2 ?? (from 0 to 2) ? = 10 ?) ∫ √??? ?? (from 1 to 4) ? = 6

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.) 2 1 6 ln(x) 1 + x dx, n = 10

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.) π/2 0 3 2 + cos(x) dx, n = 4 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule

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(3 + ex) dx, n = 8 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule

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.) π/2 0 3 1 + cos(x) dx, n = 4

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.) 5 2 cos(7x) x dx, n = 8 1 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule

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.) 2 0 e^x/ 1 + x^2 dx, n = 10 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule

Use Simpson’s Rule with n = 4 to approximate the value of the definite integral ∫4...

Use Simpson’s Rule with n = 4 to approximate the value of the definite integral ∫4 0 e^(−x^2) dx. (upper is 4, lower is 0) Compute the following integrals (you may need to use Integration by Substitution): (a) ∫ 1 −1 (2xe^x^2) dx (upper is 1, lower is -1) (b) ∫ (((x^2) − 1)((x^3) − 3x)^4)dx

Question

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the...

Solutions

Expert Solution

Related Solutions

use the a) midpoint rule, b) Trapezoidal rule, and c) the Simpsons rule to approximate the...

Explain and state the formula of (a) Trapezoidal rule, (b) the Midpoint Rule, and (c) Simpson’s...

Use the trapezoid rule, midpoint rule, and Simpson’s rule to approximate the given integrals with the...

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...

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...

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...

Use Simpson’s Rule with n = 4 to approximate the value of the definite integral ∫4...