1. ## integral

integral involving absoulte value

2. When dealing with an absolute value, it usually helps to break it into two integrals.

But the region is symmetric, so just multiply by two

$2\int_{3}^{4}(x-3)dx$

3. thank you for the very nice sketch.

after reviewing your suggestions, am I correct in saying that the integral equates to 1.

4. Hello, DINOCALC09!

If you make a sketch, you don't need Calculus!

$\int^4_2|x - 3|\,dx$
Code:
      |
\
| \
|   \
|     \                       /
|       \                   /
|         \               /
|           \           /
|           |:\       /:|
|           |:::\   /:::|
- + - - + - - + - - * - - + - - + - -
1     2     3     4     5

Got it?

5. i just find the area of the two triangles. correct?