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Use the information and data in Exercise 6.4.33 to find the work required to propel a 1000-kg space vehicle out of the earth's gravitational field.
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 8
Improper Integrals
Integration Techniques
Baylor University
University of Nottingham
Idaho State University
Lectures
01:53
In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.
27:53
In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.
05:35
Use the information and da…
0:00
01:15
02:58
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02:15
Use an improper integral a…
03:52
Compute the work $W$ again…
01:06
(a) Use an improper integr…
01:05
A $2800-\mathrm{kg}$ space…
(1II) $\mathrm { A } 2800 …
03:15
02:31
Find the work done in lift…
01:41
The gravitational force be…
02:13
Use the result of Exercise…
The problem is use the information at the data you exercise six point or pointed. There is three to find it. The work required it to probable one sound than a little grounds space. What? Michael Outift Earth Gravitational field By using the information and data in exercise six point four point three three. We have the work required. Yes. He caught you in improperly to grow from our affinity. Jean. I'm one too over. Explain the axe. Here are is he conscious? Go Ideas. Earth, This is Echo six point three seven. I have to tend to the power of six meters and he caught you. This is a gravitational constant. Six point six house tend to selective lover. You would have me square meters for kilograms. One is Earth math. This is a culture of five point nine. It times ten to the power of twenty four kilograms. I'm Tru. Is that you? One thousand killing ground now This improper integral is equal to She had one too. Hands to the limit. It goes to infinity into girl from hard to farm number A like over square. Jax, This is a good one. I'm true. That's the limit. and cost to energy. One more word. Negative one. Roll a last one over R. This is equal to G. I'm one too over our I'm implying this for wallows to this function we have. This is about six point two six. Ham's tend to the parlor of ten new tests.
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