# Area, Volume, and Arc Length

### Example 1

For each triangle,

(a) Find an integral expression for the area of the triangle using the slice and variable of integration indicated.

(b) Evaluate your integral and check that it agrees with the area you find using the formula

### Example 2

For each triangle,

(a) Find an integral expression for the area of the triangle using the slice and variable of integration indicated.

(b) Evaluate your integral and check that it agrees with the area you find using the formula

### Example 3

For each triangle,

(a) Find an integral expression for the area of the triangle using the slice and variable of integration indicated.

(b) Evaluate your integral and check that it agrees with the area you find using the formula

### Example 4

For each triangle,

(b) Evaluate your integral and check that it agrees with the area you find using the formula

### Example 5

For a triangle with base *b* and height *h*, use integration to derive the area formula

Use vertical slices with *x* for the variable of integration.