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

( 2 + 10).

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

So...how do I solve this problem?