definite integral and area
Let B(x) represent the area bounded by the graph and the horizontal axis and vertical lines at t=0 and t=x for the graph shown below. Evaluate B(x) for x = 1 and 5.
For f(x)=1/(x+1) find
Find the areas of the rectangles:
Rewrite as a definite integral. Do not evaluate.
Represent the area bounded by the regions as a definite integral and evaluate.
Your velocity along a straight line is shown below
Use Leibniz rule to find:
Use change of variables to find:
Sketch the graph of the two functions and find the area between them.
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1. Let B(x) represent the area bounded by the graph and the horizontal axis and vertical lines at t=0 and t=x for the graph shown below. Evaluate B(x) for x = 1 and 5.
Solution:
B(1) = 1/2 +1 = 3/2
B(5) = 1/2+ 1 + 1 + 1 + 1/2 +1/2 + 1 + 1/2 = ...
Solution Summary
This posting explains how to find derivative of a integral using Leibniz rule and also explains how to find area between two curves.