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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_0^4 x^3 \sin x\ dx $ , $ n = 8 $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 7

Approximate Integration

Integration Techniques

Missouri State University

Campbell University

Harvey Mudd College

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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Use (a) the Trapezoidal Ru…

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Use the Trapezoidal Rule_ …

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06:51

problem. You have it. There's no tricks here. Just calculation, right? You need a calculator. Here's a function and their tactics equal Tau four minus zero, divided by age toys. Right There actually is one. You need to know what is P. M and asked. People don't know. Just look at the book, right? Here's a T on asked. There has is equal to 1/2 and everything is already known, so just calculate you could get a correct answer here.

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