Question

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 1

Explanation:

Given

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

a)

Use the trapesoidal rule:

To find the upper bound frind
`f`:

Here,
`f(x)=10x,\,f`

So, the upper bound is
`K=10`

`|E_T|=(10(2-(-2))^3)/(12n^2)\leq 4* 10^(-4)=(53.33)/(n^2)\leq 0.0005\\\\=326.59\leq n`

so, n=326.59=327

b)

Use the simpsons rule

`K=f^4(x),\,f^4(x)=0,\, so,\, K=0\\\\|E_s|=(K(b-a)^5)/(180n^4)=0`

so, n = 2