Let f(x) = x² - 4x + 3 = (x - 1)(x - 3)…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Let . The curve is below the -axis for . Find the signed area , and then the area between the curve and the -axis from to . Give the area to four decimal places.
Need a reminder? The key ideaShow
If and is continuous on , then the signed area is . Where changes sign, split the interval and add the sizes to get the area.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The signed area. . Then .
Step 2. Split at . On the function is positive: .
Step 3. The part below the axis. On the function is negative: .
Step 4. The area. Add the sizes: .
Answer: the signed area is and the area is .
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