1. Use four boxes to approximate the area under the curve $f(x) = 3 \cos(x) + 8$ from $x = 0$ to $x = \pi$. 2. Use six boxes to approximate the area under the curve $f(x) = x^2 - 2x + 2$ from $x = 3$ to $x = 6$. 3. Find the exact area under the curve $f(x) = 5x^2$ from $x = 1$ to $x = 5$. You cannot use anti-differentiation results to do this; you must set up the sequence and take its limit. 4. Find the exact area under the curve $f(x) = 2x + 7$ from $x = 2$ to $x = 8$. You cannot use anti-differentiation results to do this; you must set up the sequence and take its limit.
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Step 1: For the first question, we need to approximate the area under the curve f = 3cos(x) + 8 from x = 0 to x = 7π using four boxes. Show more…
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