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Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral. $ \displaystyle \int \frac{\cos^{-1} (x^{-2})}{x^3}\ dx $
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 6
Integration Using Tables and Computer Algebra Systems
Integration Techniques
Missouri State University
Campbell University
University of Michigan - Ann Arbor
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 the Table of Integrals…
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Use the Table of Integral…
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Okay, This question wants us to integrate this function. So to do that, we want to transform this into the integral into one of our forms in the table. So to do this, let's make the substitution to make that transformation have. So we get you equal to X to the minus two. Because usually picking the argument of a coastline is a good start. So that makes d'you equal to negative, too. X to the minus three d x and we have X to the minus three d x. So we just gotta divide by negative too. So now we can transform are integral into negative 1/2 times the integral of co sign inverse of you, do you? And that's a much simply looking for him so we can look it up here, which gives us a formula for anti derivative. So let's just copy that down, keeping our negative 1/2 outside. So this is our anti derivative and now all we have to dio is substitute back in for you. So we get negative 1/2 times X to the negative to co sign in verse of X to the negative too minus square root of one minus X to the minus forth plus C and simplifying We get one over two X squared co sign in verse of one over X squared plus 1/2 square root one minus extra, the fourth plus C and that's your final answer.
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