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Find the approximations $ T_n $, $ M_n $, and $ S_n $ for $ n = 6 $ and 12. Then compute the corresponding errors $ E_T $, $ E_M $, and $ E_S $. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when $ n $ is doubled?
$ \displaystyle \int_1^4 \frac{1}{\sqrt{x}}\ dx $
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 7
Approximate Integration
Integration Techniques
Campbell 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.
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Okay problem 28 point: we need to find t: minus n is equal to second 12 and the corresponding errors begin to know, there's a corresponding errors and an estimate. You want to find the estimate errors. You can use this ominous, but if not you want to find a corresponding address. It'S just. I minus m r s r t right, so you need to find t m s. Here'S function p m and as just do it, you know everything you know. What f is- and you know, dirx just use the function to find p m as what happens to the errors taboo. You divided the whole interval into more pieces, so your approximation is more close to the real value, so the errors becomes smaller and if you want to know how to compute, i let me find out this 1 or square x, dx right. It is equal to x to the negative the x, so we want to find 2 times an take a derivative of this function. It becomes this function, so it is equal to this. 1 right is just a 2 times. 2. Minus 1 is just 2 point right. It'S just 2 and just compute all autocenes and compare with.
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