### Home > APCALC > Chapter 4 > Lesson 4.1.3 > Problem4-32

4-32.

Evaluate the following definite integrals without a calculator. Then write a statement about the connection between them. Check your answers with a calculator.

1. $\int _ { 2 } ^ { 9 } 8 x d x$

Sketch a graph. $y = 8x$ is a linear function, and the area between $x = 2$ and $x = 9$ is trapezoidal.

2. $\int _ { 2 } ^ { 9 } ( 8 x + 5 ) d x$

What effect does the $+5$ have on the bases of the trapezoid?

3. $\int _ { 2 } ^ { 9 } 5 d x$

Notice that the the trapezoid below the function being integrated in part (b) and above the function being integrated here is equivalent to the trapezoid you found in part (a).