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Estimate the minimum number of subintervals to approximate the value of Integral from negative 2 to 2 (5 x squared plus 4 )dx with an error of magnitude less than 5 times 10 Superscript negative 4 using a. the error estimate formula for the Trapezoidal Rule.

Answer :

fortuneonyemuwa

Answer:

Step-by-step explanation:

Given

[tex]\int\limits^2_{-2} {(5x^2+4)} \, dx \\\\Here\, f(x)=5x^2+4,[/tex]

a)

Use the trapesoidal rule:

To find the upper bound frind [tex]f"(x)[/tex]:

Here, [tex]f(x)=10x,\,f"(x)=10,\, and |f"(2)|<10[/tex]

So, the upper bound is [tex]K=10[/tex]

[tex]|E_T|=\frac{10(2-(-2))^3}{12n^2}\leq 4\times 10^{-4}=\frac{53.33}{n^2}\leq 0.0005\\\\=326.59\leq n[/tex]

so, n=326.59=327

b)

Use the simpsons rule

[tex]K=f^4(x),\,f^4(x)=0,\, so,\, K=0\\\\|E_s|=\frac{K(b-a)^5}{180n^4}=0[/tex]

so, n = 2

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