Questions: Examine the graph below. Write the formula to find the area between the curves. A. ∫(a to b) f(x) dx B. ∫(a to b) f(x)+g(x) dx C. ∫(a to b) f(x)-g(x) dx D. ∫(a to b) g(x)-f(x) dx

Transcript text: 5. $\qquad$ Examine the graph below. Write the formula to find the area between the curves. A. $\int_{a}^{b} f(x) d x$ B. $\int_{a}^{b} f(x)+g(x) d x$ C. $\int_{a}^{b} f(x)-g(x) d x$ D. $\int_{a}^{b} g(x)-f(x) d x$

Solution

Solution Steps

Step 1: Identify the upper and lower curves

The upper curve is $y=f(x)$ and the lower curve is $y=g(x)$.

Step 2: Set up the integral

The area between the curves is given by the definite integral from $a$ to $b$ of the difference between the upper and lower curves: $\int_a^b (f(x) - g(x)) dx$.

Final Answer

C. $\int_{a}^{b} f(x)-g(x) d x$

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