Volume of Perpendicular Slices for Region Bounded by y=e^x and x=1

You have correctly set up the volume of a slice perpendicular to the x-axis as the integral of the function (e^x)^2, or e^(2x), from 0 to 1. This should give you the correct answer. In summary, the conversation discusses finding the volume of a solid created from a region bounded by y=e^x, the x-axis, the y-axis, and the line x=1. The volume of a slice perpendicular to the x-axis is found by taking the integral of the function e^(2x) from 0 to 1.
  • #1
ada0713
45
0
finding volume by integration

Homework Statement



Consider the region bounded by y=e^x, the x-axis, the y-axis, and the line x = 1. A solid is created so that the given region is its base and cross-sections perpendicular to the x-axis are squares. What is the volume of a slice perpendicular to the x-axis?


The Attempt at a Solution



since the regions is bounde by y=e^2, y=0. and x=1,
doesn't the volume of a slice perpendicular to the x-axis
has to be (e^x)(e^x)dx ..(since the base and height are equal)

so the answer should be [Integral from 0 to 1](e^(2x)) dx


Am I wrong? I thought I set it up right but the webassign thing's
keel saying that somethings wrong

I'm in a hurry so please help!
amd
 
Last edited:
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  • #2
That looks correct to me.
 

What is "Finding Volume by Integration"?

"Finding Volume by Integration" is a method used in calculus to determine the volume of a three-dimensional object by using mathematical integration.

Why is "Finding Volume by Integration" useful?

"Finding Volume by Integration" is useful because it allows scientists to calculate the volume of irregularly shaped objects that cannot be easily measured using traditional methods.

What are the steps involved in "Finding Volume by Integration"?

The steps involved in "Finding Volume by Integration" include:

  1. Identifying the object and the boundaries of the volume to be calculated.
  2. Expressing the boundaries as a mathematical function.
  3. Setting up the integral to integrate the function over the given boundaries.
  4. Solving the integral to obtain the volume.

What are some common applications of "Finding Volume by Integration" in science?

"Finding Volume by Integration" is commonly used in fields such as physics, engineering, and chemistry to calculate the volume of complex shapes and objects, such as fluid containers, 3D models, and chemical solutions.

What are some limitations of "Finding Volume by Integration"?

Some limitations of "Finding Volume by Integration" include the need for advanced mathematical skills and the assumption of a constant density throughout the object. It may also be time-consuming for complex objects with irregular boundaries.

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