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Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral.

$ \displaystyle \int_0^{\frac{\pi}{2}} \cos 5x \cos 2x\ dx $ ; entry 80

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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

Harvey Mudd College

University of Nottingham

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.

01:11

$1-4$ Use the indicated en…

05:25

Use the Table of Integrals…

03:35

02:51

04:21

05:41

04:04

01:16

03:20

03:28

Okay, so this question wants us to evaluate this integral using a table so we can see this Integral is of the former co sign of something Times Co sign of another something. So we find this formula in the integral table that just tells us. But the co sign of a ex co signed B X has the following integral. So now all we need to dio is find our values of A and B, which, of course, are just the numbers in front of the ex. So our first angle is five, and our second is too. So now this means are integral Combs. In this case, sign of five plus two is seven x divided by, well, two times seven, which is 14 minus sign of three x over two times three, which is six. So now this becomes our indefinite integral so are anti derivative. So now we can plug that in over here. So it's sign of seven X over 14 minus sorry plus sign of three X over six, and we're evaluating that it zero and that pirate too. So the easy cases zero, because we just have signed functions. So the zero term vanishes. So we just need to find pi over to plugged into this expression. So what is sign of seven pi over too? Well, that's just to pie. Plus negative three plus three pi over too. Sorry. So it's gonna come out to negative one. So we get negative one over 14 minus another one over six from the three pi over, too. And negative. 1/14 minus 1/6 is five over 21 with a negative sign in front, of course.

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