SOLUTION: Consider the integral 2 1[19 - 4x dt. (a) Using the trapezoidal rule with 4 subintervals, estimate the integral numerically. (b) Find the integral exactly (using calculus and

Question 1140897: Consider the integral 2 1[19 - 4x dt.
(a) Using the trapezoidal rule with 4 subintervals, estimate the integral numerically.
(b) Find the integral exactly (using calculus and showing the working) and compare
this with your numerical result by calculating the absolute value of the error.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I read this as the integral from 1 to 2 of (19-4x). [(dx..., not dt)]

The interval 1 to 2 with 4 subintervals means the x values of the endpoints of the intervals are 1, 1.25, 1.5, 1.75, and 2.

The function values at those endpoints are 15, 14, 13, 12, and 11.

The integral by the trapezoidal rule is

The indefinite integral of the function using calculus is

The definite integral for the interval 1 to 2 is

The "estimate" using the trapezoidal rule is exactly the same as the result using calculus. This is as it should be, because the given function is linear. For any linear function, the trapezoidal rule will give the exact integral.
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