Question

The black curve f and red line g intersect at x=2, 4, and 6. Which sum of integrals gives the total shaded area from 0 to 8?

Accepted Answer

$$\begin{aligned}&-\int_{0}^{2} (f(x)-g(x))\,dx\ &+ \int_{2}^{4} (f(x)-g(x))\,dx\ &- \int_{4}^{6} (f(x)-g(x))\,dx\ &+ \int_{6}^{8} (f(x)-g(x))\,dx\end{aligned}$$

Answer

$$\begin{aligned}&-\int_{0}^{2} (f(x)-g(x))\,dx\ &+ \int_{2}^{8} (f(x)-g(x))\,dx\end{aligned}$$

Answer

$$\begin{aligned}&\int_{0}^{8} (f(x)-g(x))\,dx\end{aligned}$$

Answer

$$\begin{aligned}&\int_{0}^{2} (f(x)-g(x))\,dx\ &- \int_{2}^{4} (f(x)-g(x))\,dx\ &+ \int_{4}^{6} (f(x)-g(x))\,dx\ &- \int_{6}^{8} (f(x)-g(x))\,dx\end{aligned}$$

Practice: Integration - Multiple Intersections Graph to Area Setup

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Practice:

Integration - Multiple Intersections Graph to Area Setup