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    definite integral and area

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    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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    https://brainmass.com/math/functional-analysis/definite-integral-area-616772

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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.

    $2.19