Subjects calculus

Area Between Lines

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Area Between Lines


1. The problem involves finding the area between the curves defined by $y=6$ and $y=3$. 2. Since both curves are horizontal lines, the area between them over any interval on the x-axis is the difference in their y-values multiplied by the length of the interval. 3. To find the exact area, the bounds along the x-axis must be specified. Without x-bounds, we can only express the area per unit length in $x$. 4. The vertical distance between the two lines is $6-3=3$. 5. Therefore, the area between $y=6$ and $y=3$ over an interval from $x=a$ to $x=b$ is: $$\text{Area} = (6-3) \times (b - a) = 3(b - a)$$ 6. Without specific $x$-bounds, the answer is the formula above expressing area as a function of the length of the interval in $x$.