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Evaluate the integral.
$ \displaystyle \int^{\pi/4}_{0} \frac{1 + \cos^2 \theta}{\cos^2 \theta} \,d\theta $
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00:35
Frank Lin
01:11
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 4
Indefinite Integrals and the Net Change Theorem
Integration
Missouri State University
Oregon State University
University of Michigan - Ann Arbor
Boston College
Lectures
05:53
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.
40:35
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.
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How to evaluate this integ…
So here it might be helpful to split this term into. So we can write see pie. I can't write pie 54 So you can write first term as one over costa and squared fair plus Co sounds great of theater. Overcoat sounds great of data. So this is just the one and so one of the coast and square theater to. That's right. This first that will just be secret squared theater plus one again to put these parentheses. And so if we look to the table of indefinite air girls, we can see that sequence squared. Theta is just equal to the integral of secret squared. The theater will be tangent theater. So here what's right tangent theater A derivative of one will be theta. A profound pi over four. Lower bound of zero. It's not about you. Right? Tangent of pipe before Plus pi over four- Attention of zero plus zero. So tangent of pie before This will be one plus pi over four. My extension of 00 plus zero. Also zero. So he gets plus one plus pi over four.
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