Definite Integrals Exercises

Answer

We divide [0, 9] into 3 sub-intervals of width 3. The first trapezoid has

The second trapezoid has

The third trapezoid has

Adding up the areas of the trapezoids, we get

71.625 + 58.125 + 31.125 = 160.875.

This is an underestimate, since the trapezoids don't cover the whole area between f and the x-axis on [0, 9].

Answer

Each sub-interval has width 0.25.

First trapezoid, on [0, 0.25]:

Second trapezoid, on [0.25, 0.5]:

Third trapezoid, on [0.5, 0.75]:

Fourth trapezoid, on [0.75, 1]:

We add the areas of the trapezoids and get

0.75 + 1.25 + 1.875 + 2.5 = 6.375.