### Home > APCALC > Chapter 4 > Lesson 4.1.2 > Problem4-18

4-18.

Evaluate the following definite integrals.

1. $- \int _ { 0 } ^ { 3 } x d x$

Ignoring the negative for the moment, sketch and shade

$\int_{0}^{3}xdx.$

The area under the curve is a triangle with base $3$ and height $3$. Find the area ... then make it negative.

2. $\int _ { 0 } ^ { 3 } ( - x ) d x$

The area of the triangle is below the $x$-axis. Does this make it positive or negative?

3. $\int _ { 3 } ^ { 0 } x d x$

Notice that the integrand is the same as in part (a); but the bounds have flipped, causing you to look at the base of the triangle from right to left. This will make the area negative.

4. $- \int _ { 3 } ^ { 0 } ( - x ) d x$

Think through all the negatives and reverse bounds. Is there a way to rewrite this integral so it will be simpler to sketch and evaluate?