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Evaluate the integral.
$ \displaystyle \int \theta \tan^2 \theta\ d \theta $
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 5
Strategy for Integration
Integration Techniques
Missouri State University
Oregon State University
Harvey Mudd College
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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Evaluate the integral.…
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Evaluate the indefinite in…
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Find the indefinite integr…
let's use by parts here. Neuticles Data, D'Oh and then for Devi. So then, from here, we need to integrate chance. Where's so Use one of the Pythagorean identities to rewrite this. And then we have cantina minus data. So recall the formula for parts U V minus integral B to you. So let's plug in our U and V and then minus in a girl. And that here we have tan theta minus Dana and then data and will simplify that in a roll of ten. That's natural. Log absolute value. See, Cam. And then here you have a double minus so that'LL be plus and then finally just combine this with this and that's our answer.
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