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Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take $ C = 0 $).
$ \displaystyle \int \tan^2 \theta \sec^2 \theta \, d\theta $
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Calculus 1 / AB
The Substitution Rule
Missouri State University
In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.
In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.
Evaluate the indefinite in…
evaluate the integral, and…
given the fact that are you is tan of data. This means that d u over D thing that's the same thing is do you over dx except for instead of X. They've got data on this context is seeking square data. Therefore, we know that d you just written in terms of do you a secret scrub data d theta. Now we have the integral of you scored. Do you? We can integrate this to BU cubed over three years in the power rule, increased export by one divide by the new exponents And now back substituting end we end up with are integral now chek of our answers Reasonable weaken graph and you can see over here this is a reasonable answer.
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