Find the absolute value of the resulting error if the value of is estimated with 3 trapezoids of equal width.

Question

Find the absolute value of the resulting error if the value of  is estimated with 3 trapezoids of equal width.

anonymous · Answer

https://i.gyazo.com/f2e9857f2f03dc33817cd1f50f06633b.png

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

were you able to calculate the trapezoidal area? or the exact area?

anonymous · Answer

No, how would I do that?

jim_thompson5910 · Answer

are you familiar with this rule?
$$\Large \int x^n dx = \frac{x^{n+1}}{n+1} + C$$

anonymous · Answer

Yes

kenshin · Answer

If you integrate the whole thing it becomes (1/4)x^(4) |0 to 3, which is  81/4
by trapezoidal rule to estimate, you just add up the area under the curve in trapeziums, in this case, 3 intervals are, between 0 to 1, 1 to 2, and 2 to 3. so (0+1)/2 + (1+2^3)/2 + (2^3+3^3)/2 gives you 90/4, the error is therefore 9/4 and that's 2.25

anonymous · Answer

Can you confirm @jim_thompson5910 ? His explanation definitely matched my thoughts here

jim_thompson5910 · Answer

yes @Kenshin is correct

anonymous · Answer

Thank you @Kenshin and @jim_thompson5910