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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_0^2 \frac{1}{1 + x^6}\ dx $ , $ n = 8 $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 7

Approximate Integration

Integration Techniques

Oregon State University

Harvey Mudd College

Baylor University

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.

12:43

Use (a) the Trapezoidal Ru…

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06:51

A problem, a that's the same, you need a calculator. What is t what is, and what is this? Here'S a t t, here's m t s that you can calculate just calculate. Third: half is equal to 1 over 4 right because it's 2 over 8 and everything x, 2 minus x 1 is equal to the right 1 over 4 pi just calculate calculate calculate you can get the correct answer. Here'S the correct answer:

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