Estimate area, 4 right endpoints and rectangles. Is this an overestimate or underestimate?
\(\displaystyle f(x) = 5\sqrt{x}\) on interval \(\displaystyle [0,4]\) given \(\displaystyle [a, b]\)
\(\displaystyle \sum\limits_{i=4}^n \Delta x [f(a + i \Delta x)]\)
\(\displaystyle \Delta x = \dfrac{b - a}{n}\)
\(\displaystyle \Delta x = \dfrac{\dfrac{4} - 0}{4} = 1\)
\(\displaystyle n = 4\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[f(0 +(1)(1)] + [f(0 +(2)(1)] + [f(0 +(3)(1)] + [f(0 +(4)(1)]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[f((1)(1)] + [f((2)(1)] + [f((3)(1)] + [f((4)(1)]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[f((1)] + [f((2)] + [f((3)] + [f((4)]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[5\sqrt{(1)}] + [5\sqrt{(2)}] + [5\sqrt{(3)}] + [5\sqrt{(4)}]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[5(1)] + [5\sqrt{2}] + [5\sqrt{3}] + [5(2)]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[5] + [5\sqrt{2}] + [5\sqrt{3}] + [10]]\)
\(\displaystyle \sum\limits_{i=4}^n [[5] + [5\sqrt{2}] + [5\sqrt{3}] + [10]]\) On the right track?
\(\displaystyle f(x) = 5\sqrt{x}\) on interval \(\displaystyle [0,4]\) given \(\displaystyle [a, b]\)
\(\displaystyle \sum\limits_{i=4}^n \Delta x [f(a + i \Delta x)]\)
\(\displaystyle \Delta x = \dfrac{b - a}{n}\)
\(\displaystyle \Delta x = \dfrac{\dfrac{4} - 0}{4} = 1\)
\(\displaystyle n = 4\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[f(0 +(1)(1)] + [f(0 +(2)(1)] + [f(0 +(3)(1)] + [f(0 +(4)(1)]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[f((1)(1)] + [f((2)(1)] + [f((3)(1)] + [f((4)(1)]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[f((1)] + [f((2)] + [f((3)] + [f((4)]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[5\sqrt{(1)}] + [5\sqrt{(2)}] + [5\sqrt{(3)}] + [5\sqrt{(4)}]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[5(1)] + [5\sqrt{2}] + [5\sqrt{3}] + [5(2)]]\)
\(\displaystyle \sum\limits_{i=4}^n (1) [[5] + [5\sqrt{2}] + [5\sqrt{3}] + [10]]\)
\(\displaystyle \sum\limits_{i=4}^n [[5] + [5\sqrt{2}] + [5\sqrt{3}] + [10]]\) On the right track?
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