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Find the escape velocity $ v_0 $ that is needed to propel a rocket of mass $ m $ out of the gravitational field of a planet with mass $ M $ and radius $ R $. Use Newton's Law of Gravitation (see Exercise 6.4.33) and the fact that the initial kinetic energy of $ \frac{1}{2} mv^2_0 $ supplies the needed work.
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 8
Improper Integrals
Integration Techniques
Missouri State University
Campbell University
University of Michigan - Ann Arbor
University of Nottingham
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.
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