Limits and Integrals In Exercises 73 and 74, evaluate the limit and sketch the graph of the region whose area is represented by the limit. lim ‖ Δ ‖ → 0 ∑ i = 1 n ( 4 − x i 2 ) Δ x , where x i = − 2 + 4 i n and Δ x = 4 n
Limits and Integrals In Exercises 73 and 74, evaluate the limit and sketch the graph of the region whose area is represented by the limit. lim ‖ Δ ‖ → 0 ∑ i = 1 n ( 4 − x i 2 ) Δ x , where x i = − 2 + 4 i n and Δ x = 4 n
Solution Summary: The author explains how to calculate the given limit and sketch the graph of the region whose area is represented by it.
Using the Fundamental Theorem of Calculus find the area of the region bounded by the x-axis and the graph of f(x)=−x2−1x+12.
Computing areas Use a double integral to find the area of thefollowing region.
The region bounded by the spiral r = 2θ, for 0 ≤ θ ≤ π, and the x-axis
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find the area of the region completely enclosed by f(x)=x+5 and g(x)=x^2+x-4 in the region.
a) Show that the limits of integration are a=-3, b=3 using algebra, not by plugging in those values in f(x) and g(x).
b) Find the area of the region. Use a=-3, b=3
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY