Question

Find the area under the given curve over the indicated

interval.
y = 6; [1, 5]
The area under the curve is. (Simplify your answer.)
Ay
7
6-
5432:
5-
4-
3-
2-
1-
0123456
X
N

Answer 1

The area under the curve y = 6 between x = 1 and x = 5 is calculated as the area of a rectangle with base 4 and height 6, resulting in 24 square units.

Step-by-step explanation:

When you are asked to find the area under the curve y = 6 over the interval [1, 5], this is actually a straightforward problem because y is a constant function. Since y doesn't change, the graph of y = 6 is a horizontal line, and the area under this line from x = 1 to x = 5 is a rectangle. You find the area of a rectangle by multiplying the base by the height. Here, the base is the length of the interval on the x-axis, which is 5 - 1 = 4, and the height is the constant value of y, which is 6. Therefore, the area under the curve is 4 * 6 = 24 square units.