Subjects calculus

Area Enclosed 368593

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Area Enclosed 368593


1. **State the problem:** Find the area of the region enclosed by the curves. 2. **General formula:** The area between two curves $y=f(x)$ and $y=g(x)$ from $x=a$ to $x=b$ is given by $$\text{Area} = \int_a^b |f(x) - g(x)| \, dx$$ 3. **Important rules:** - Identify the points of intersection to find limits $a$ and $b$. - Determine which function is on top (greater value) in the interval. - Set up the integral accordingly. 4. **Intermediate work:** - Find intersection points by solving $f(x) = g(x)$. - Determine $f(x) - g(x)$ or $g(x) - f(x)$ depending on which is greater. - Compute the definite integral. 5. **Explanation:** The area between curves is the integral of the vertical distance between them over the interval where they enclose a region. By integrating the difference, we sum up all the infinitesimal strips of area. Since the specific curves are not provided, this is the general method to find the enclosed area.