Purchase Solution

definite integral and area

Not what you're looking for?

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.

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.

Solution Preview

Hi,

Please find detailed solution attached herewith.
I hope it will help you. I will be happy to assist you in future.

Thanks

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 provided by:
Education
• BSc, Meerut University
• MSc, Meerut University
• MPhil, Institute of Advanced Studies
• MSc, AIT
Recent Feedback
• "Perfect, thank you so much!!! I will definitely request you in the future! You are amazing!"
• "Thank you. "
• "Thank you so much I have two more that I need your help with if your available."
• "Thank you, I was wondering why you rejected me the first time."
• "Thanks again."

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.