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Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of $ n $. (Round your answers to six decimal places.)

$ \displaystyle \int_2^3 \frac{1}{\ln t}\ dt $ , $ n = 10 $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 7

Approximate Integration

Integration Techniques

Harvey Mudd College

University of Michigan - Ann Arbor

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.

14:35

Use (a) the Trapezoidal Ru…

00:32

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01:25

13:18

12:53

07:21

03:41

11:43

09:13

00:30

11:59

16:15

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12:03

problem. 14. This is just another punk days off calculation. There's no tricks here. Just calculate average, change everything. It's already know it. Here's a function and their taxis three minus two, divided by 10 days. One or 10. Right. And here the T have a nasty just calculate, calculate and calculate. Everything is already knowing you could gather crackdowns. They're here.

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