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Evaluate the integral.
$ \displaystyle \int_0^{\frac{\pi}{2}} \cos^2 \theta d \theta $
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 2
Trigonometric Integrals
Integration Techniques
Oregon State University
Harvey Mudd College
University of Nottingham
Idaho State University
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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answer the following?
this problem is from Chapter seven, Section two. Problem number seven in the book Calculus Early Transcendental Sze, eighth Edition. My James Dorf. So here we have a definite integral from zero pie over two of co sign squared of theta D data. So since there's no signs in this problem, it's only a co sign, and it's an even power. It's going to be useful to use this trick to metric identity for co science, where SOCO Sign Square is one plus co sign of two data, all divided by two. So we simply replaced co sign squared with this other expression tohave integral from zero to Piper, too. And then we have a one half plus co sign to date over, too. So now let's integrate these from separately. So one half the integral that just becomes data over to and for the other term, this becomes science with NATO over four, and this is coming from the use up u equals to data, and we're evaluating this new expression zero and powerful, too. So it's played by over to first for the so we have a power for plus sign two times Pi over to is just pie. So sign a pie over four and now we plug it zero as well. When we plug in zero for data, we have a zero for two plus sign of zero over four. So using our knowledge from the unit Circle and trick, we know that Santa Pie a zero sign of zero zero. Sorry. Final answer paper for
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