Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Evaluate the integral.
$ \displaystyle \int_0^{\frac{\pi}{6}} \sqrt{1 + \cos 2x} dx $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by J Hardin
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 2
Trigonometric Integrals
Integration Techniques
Missouri State University
Oregon State University
University of Nottingham
Boston 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.
01:24
Evaluate the integral.…
06:01
Evaluate the integrals.
02:43
00:53
Evaluate the definite inte…
04:02
02:50
Evaluate the integrals…
01:29
01:39
05:15
03:59
this problem is from Chapter seven section to a problem. Number forty five in the book Calculus Early Transcendental lt's a Condition by James Store. We hear we have a definite integral of the square of one plus coast high to X. So here let's talk about co sign of two X. We can use a double ankle formula to rewrite this as two times co sign squared X minus one. Then from here we have one plus coastline to X. Here we can cancel the ones and we just have to co sign Squared X. Then we could take the square root so we can write. This is I want to times the square room of Coastline Square, which isn't necessarily co sign because technically, the square root of the square is going to be the absolute value. So this case, we should to be safe. You should always write absolute value there, I guess in general, the rule that I'm using here is squirt of a square is absolute value in our problem. However, this will be actually will simplify too, two times called radical two times co sign since coastline eggs. It's positive in our inseparable of the liberation. What that said we can rewrite are integral. That becomes zero time for six time's radical, too times cosine x so you can pull out the rat radical to outside the integral if you like. So Integral co sign a sign so they get radical, too time. Sinus evaluated at zero and pi over six. So sign of viruses. One half and sign of zero zero So we get squared or two divided by two, and that's our answer.
View More Answers From This Book
Find Another Textbook
01:27
Use the Distributive Property to remove the parentheses.$$(x-4)(x-2)…
00:46
True or False $\sqrt[5]{-32}=-2$
01:12
True or False $\sqrt[4]{(-3)^{4}}=-3$
01:54
Write each number in scientific notation.$$32,155$$
01:03
Explain why $\frac{4+3}{2+5}$ is not equal to $\frac{4}{2}+\frac{3}{5}$
01:08
Write each number as a decimal.$$9.7 \times 10^{3}$$
00:48
Write each number as a decimal.$$9.88 \times 10^{-4}$$
01:11
If $2=x,$ why does $x=2 ?$
If $x=5,$ why does $x^{2}+x=30 ?$
01:19
Write each number as a decimal.$$1.1 \times 10^{8}$$
