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Use (a) the Midpoint Rule and (b) Simpson's Rule to approximate the given integral with the specified value of $ n $. (Round your answers to six decimal places.) Compare your results to the actual value to determine the error in each approximation.
$ \displaystyle \int_0^\pi x cos x\ dx $ , $ n = 4 $
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Calculus 2 / BC
Techniques of Integration
Missouri State University
Oregon State University
Harvey Mudd College
University of Nottingham
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.
In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.
Use (a) the Midpoint Rule …
Use (a) the Trapezoidal Ru…
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