5.1: Approximating Areas
- Page ID
- 144292
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- Compute \(\displaystyle \sum_{i = 1}^{10} 2i\).
- Compute \(\displaystyle \sum_{k = 3}^{7} (k^2 - 2k +1)\).
- Use a left-endpoint sum with \(n = 4\) subintervals to approximate the area under \(f(x) = \dfrac{1}{x - 1}\) on \([2, 3]\).
- Use a right-endpoint sum with \(n = 4\) subintervals to approximate the area under \(g(x) = \cos(\pi x)\) on \([0, 1]\).
- Use a left-endpoint sum with \(n = 8\) subintervals to approximate the area under \(h(x) = \sqrt{16 - x^2}\) on \([0, 4]\).
- Use a right-endpoint sum with \(n = 8\) subintervals to approximate the area under \(h(x) = \sqrt{16 - x^2}\) on \([0, 4]\).
- Use a midpoint sum with \(n = 8\) subintervals to approximate the area under \(h(x) = \sqrt{16 - x^2}\) on \([0, 4]\).
- Use formulas from geometry to calculate the exact area under \(h(x) = \sqrt{16 - x^2}\) on \([0, 4]\). [Hint: First graph the function.]