# 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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#### Solution Preview

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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.