2) Use the integral below to answer the following questions. Relative work must be clearlyshown in order to receive any credit.AX 2-a1.5sin(x2)dxa)Using n = 4, use Trapezoidal Rule to estimate the integral.b) Using n 4, use Midpoint Rule to estimate the integral.Find an n where Midpoint Rule would guarantee estimation within 6 decimal places.c)4x- 15 27

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Asked Jun 25, 2019
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C). Find an 'n' where Midpoint Rule would guarantee estimation within 6 decimal places.

2) Use the integral below to answer the following questions. Relative work must be clearly
shown in order to receive any credit.
AX 2-a
1.5
sin(x2)dx
a)
Using n = 4, use Trapezoidal Rule to estimate the integral.
b) Using n 4, use Midpoint Rule to estimate the integral.
Find an n where Midpoint Rule would guarantee estimation within 6 decimal places.
c)
4x- 15 27
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2) Use the integral below to answer the following questions. Relative work must be clearly shown in order to receive any credit. AX 2-a 1.5 sin(x2)dx a) Using n = 4, use Trapezoidal Rule to estimate the integral. b) Using n 4, use Midpoint Rule to estimate the integral. Find an n where Midpoint Rule would guarantee estimation within 6 decimal places. c) 4x- 15 27

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Expert Answer

Step 1

Let's get the concepts in place, before we proceed to solve this.

For an integral I (as shown on the white board), the error EM under mid point rule is as given by the expression on the whiteboard.

“h” used in the expression has been defined further.

“n” is what we have to find such that EM ≤ 10-6

f(x) = sin(x2)dx

a = 0, b = 1.5

Step 2

We now proceed to calculate the double derivative of f(x). Recall

  • the chain rule of calculus
  • d(sinz)/dz = cosz
  • : d(xn) / dx = nxn-1 

Please see the white board.

 

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f(x) sin()dx f'(x) 2xcos(x2) f"(x) 2 cos(x-4x2sin(x2)

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Step 3

In order to get the maximum value of f''(x), we need to plot f''(x) w.r.t over x = 0 to x = 1.5.

Please see the graph on the white board.

The maximum absolu...

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Plot of f"(x) overx 0 to x 1.5 2 0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 R -10

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