# Thread: Trapezoidal Rule with uneven subintervals

1. ## Trapezoidal Rule with uneven subintervals

This is given:
f(1)= 2
f(5)= 10
f(8)= 13
f(12)= 17

Use trapezoidal approximation to find the area of the curve described by the function values above.

I understand that I need to find the area of all the trapezoids manually. I cannot apply the normal rule because the subintervals are different.

I used the height as the difference between 1 and 5 and the bases as 2 and 10, whcih plugged into the formula for the area of a trapezoid is $\displaystyle \frac{1}{2}$( 2 + 10).

I followed this pattern but my answer was clearly off. It was WAY too big.

So...how do I solve this problem?

2. Originally Posted by Truthbetold
This is given:
f(1)= 2
f(5)= 10
f(8)= 13
f(12)= 17

Use trapezoidal approximation to find the area of the curve described by the function values above.

I understand that I need to find the area of all the trapezoids manually. I cannot apply the normal rule because the subintervals are different.

I used the height as the difference between 1 and 5 and the bases as 2 and 10, whcih plugged into the formula for the area of a trapezoid is $\displaystyle \frac{1}{2}$( 2 + 10).

I followed this pattern but my answer was clearly off. It was WAY too big.

So...how do I solve this problem?

Using trapesoid rule area from $\displaystyle 1$ to $\displaystyle 5$ is $\displaystyle 4 \times \frac{2+10}{2}=24$.

area from $\displaystyle 5$ to $\displaystyle 8$ is $\displaystyle 3 \times \frac{10+13}{2}=34.5$

area from $\displaystyle 8$ to $\displaystyle 12$ is $\displaystyle 4 \times \frac{13+17}{2}=60.$

RonL

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# trapeizodal rule of areas with uneven intervals

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