Subjects calculus

Area Expression

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Area Expression


1. The problem asks to find an expression for the area of the shaded region. 2. To find the area of a region bounded by curves, we use the formula for the area between two functions $f(x)$ and $g(x)$ over an interval $[a,b]$: $$\text{Area} = \int_a^b |f(x) - g(x)| \, dx$$ 3. Important rules: - Identify the upper and lower functions correctly. - Determine the limits of integration $a$ and $b$. - If the functions cross, split the integral at the points of intersection. 4. Without specific functions or limits given, the general expression for the shaded area is: $$\text{Area} = \int_a^b (\text{upper function} - \text{lower function}) \, dx$$ 5. If you provide the functions and interval, I can help compute or simplify the expression further.