evaluate-the-integrals-int_-pi-2pi-2-cos-x-cos-7-x-d-x

Question

Evaluate the integrals.
$\int_{-\pi / 2}^{\pi / 2} \cos x \cos 7 x d x$

Enkhzaya Enkhtaivan · Accepted Answer

So we&#x27;re a problem. 8.3 56. The intruder is from native priority to two priors to curse. Sign specs. Car sign. Cernak sticks. No, In this situation, pretty much the only thing it can do is to use the double angle. Now, the product off trick functions into somewhere different trick functions from. So, um, we have to co science courses. Next time scores are seven X. This is a call to co signer express. So next plus cursed sign. Oh, ex miner Cyrix here. So this is months we&#x27;ve done this. The West isthe really simple. So 1/2 comes out negative tires, too. Hi. Over too to the first term is cursed Sign of eight x Second term was co sign of negative 66 But Carson isn&#x27;t even functions. So I would congest in place that with your sign of six sects D x now it can now we could find anti jury. There&#x27;s immediate. So there would be negative one over 6 10 Um, excuse me, Not Nadir&#x27;s. So their antidote, of course. Science sign. So it&#x27;s native whenever 16 Because it comes out for from the chain rule sign of eight X plus one over 12 sign off six sects and evaluated at Dan Points. So so the answer would turn out to be, Let&#x27;s see at pie over to we have from the term sign of eight X at both end points you have native for pie or for pie, at which point sign is zero. So this would be you&#x27;re 16 times Cyril minus zero, and that&#x27;s six x two we have. We&#x27;ll get three pie and they&#x27;re through pine, both of which are zero. Remember any hole multiple of pie? Give zero for a sign. So the answer to her now 20

Robert Daugherty · Answer

Section eight dot to problem number 58 the integral from negative pirate to defy over too co sign of ex co sign of seven X. Okay, just a mental check. That&#x27;s an even function co sign of X Times Co sign of seven X. I&#x27;m integrating over a symmetrical Inderal Negative. Prior Batuta prior to that had better be zero or I&#x27;ve done something wrong. So I&#x27;m expecting my answer to zero when I get this, but I&#x27;ve gotta prove that. So let&#x27;s go ahead and let&#x27;s work on the anti derivatives. So how do I integrate the co sign of X Co sign of seven X The ex Well, I have to rely on the formula that the co sign of M X times to co sign of N X is equal to 1/2 the co sign of M minus in of X plus the co sign impl us in of Pecs. So that will allow me to integrate because it turns that product into a sum which is much easier, easily integrated. So this becomes this interview is 1/2 so it&#x27;s gonna be co sign. So here I&#x27;ve got M is equal to one and in is equal to seven. So this is the CO sign minus six x plus the co sign of eight x dx. Now the coastline is an even function to the coastline of minus six. X is the co sign of six X so I can rewrite this as this is 1/2 co sign of six X close 1/2 the integral of the co sign seven x the ex and servant that didn&#x27;t do a typo. It was eight x sorry with it. So that was an eight X Make that change instead of a seven eight X Now we&#x27;re ready to integrate. So this becomes 1/2 times when you integrate the co sign, you get the sign of six X divided by 16 waas 1/2 You know, Great. The co sign here again and you&#x27;re gonna have the sign of eight x times 1/8 plus a constant of integration. So this is 1 12 sign of six specs plus 1/16 sign of eight x plus a constant of integration. So that was 1/16. So that is the answer to our anti derivative. We were looking for a definite interval, so we now know that this is going to be 1 12 sign of six X plus 1/16 sign of eight X evaluated from negative pirate too, Too high or too. Now, it&#x27;s just a matter of doing the arithmetic. So sign of Pirates of six when you substitute pie or two into this equation six Pirate two. That&#x27;s three pie. The sign is going to be zero. In that case, you&#x27;re gonna have zero eight pi over to its four pi sign. There&#x27;s gonna be zero minus substitute. Negative pirate, too. So that&#x27;s gonna be the sign of negative three pie again. That&#x27;s gonna be a zero. And the sign of negative for pie again, that&#x27;s going to be a zero. This answer turns out to be zero.

Amit Srivastava · Answer

reduction Father. Five i to It&#x27;s a sign him. It&#x27;s will be and minus one in my industry insolence by am and minus two and minus both insulin. So now come to the questions You were too. Bye bye to sign seven. So seven minus one seven minus three seven. Minus my They&#x27;re so and in denominators. 77 minutes. Hi. Now so final answer will be a six into food. It took two by seven into five. 16 by 30. Site is the

Uma Kumari · Answer

here. In this problem, we are given the integral with the limit minus fiber to fiber to no sign eggs into assigned. Seven. It&#x27;s into the by using the Formula Co. Sign came into its in two design. Ending two X is equal to one upon to into design and minus and into X plus cousin M Plus n in two weeks. By applying this formula VK one upon to in to integrate with the limit minus fiber to fiber to co sign X minus seven X Plans co sign X Plus seven x into the X it would be equals two one upon to into integral with the limit minus bye bye to bye bye to cause I minus 66 into the X plus when upon to into integral with the limit minus bye bye to fiber to Because I know militates into the eggs, which is equals toe one upon to into integral with the limit minus bye bye toe by by two. Because I, minus 66 will become designed in 266 in 28 last one upon to into integral with the limit minus 5 to 5 I to assign a Texan today since because I minus tita is equals toe cause I in tetum integration off these functions are valuable to into science six x divided by six with the limit minus bye bye bye bye to plus one upon to into signed eight x divided by eight with the limit minus fiber to fiber to By putting the up a global limits, we get vulnerable 12 into science six by divided by two minus sign minus. It&#x27;s by divided by two plus one upon 16 into sign aid into bye bye to minus signed minus eight Bye bye to by simply find it we did one upon 12 into sign 35 plus sign three by plus one upon staying into signed for by plus sign for by my substituting the values we gave one upon 12 into signed three by zero plus sign three by zero plus one upon sit staying into sign fall by zero plus sign for by zero. But simplifying it we give to you therefore the value of the integral, with the limit minus five toe five to cosigned eggs in 2007 eggs into the X is equal to zero. This is the final answer

Daniel Mcconnell · Answer

So here we&#x27;re being asked to evaluate the integral to x co sign of X d. X from zero to pi eso. Let&#x27;s start out by doing. We&#x27;re Ernie&#x27;s integration by parts for this one because I think that&#x27;s the easiest way. Um, so let&#x27;s let&#x27;s make our you equal to X because that&#x27;ll help get rid of our X here and some of our problems so we can find the end to it. Um So, Mike, are you equal to X and R D V is going to be equal to the co sign of X. Um, now, after reading this, we find our do you is going to be just d X and then we find that our V is going to be co sign. It&#x27;s negative sign. So that would mean that this would be equal to the sign of X. Uh, because it&#x27;s positive. So now that we know this, we ever you envy, we write that out. X sign of X is going to be our first part of this. And they were going to subtract the integral of RV Sign of X. Do you, uh, which is going to be DX eso now? We can integrate our sign of X and that&#x27;s going to become negative co sign of X and we get X sign of X and then that&#x27;s going to be minus a negative co sign of X because CNET role of sign of excess negative sine x Ah speaking Streit plus CO sign of X. Now we have to plug in pie and zero to find out our answer to this. So it&#x27;s broken pie. First we get pie times the sign of hi plus co sign of pie. All right, so we know that the sign of pie is going to be equal to zero because we&#x27;re falls on the unit circle pie is gonna be here. Um, so we know that sign is going to be equal to zero at this point. Um, because there&#x27;s, like, no height at all. So then that means that this all become zero and our coastline of pies went beagles Who? Negative one. So we have this coming out to negative one, and then we need to subtract our second part where we plug in zero to everything in here. So we would be zero times the sign of zero plus the CO sign of zero. So zero times sign of zero and being zero, and our coastline of zero is going to be a one. So we get negative one minus one. And our answer to this problem is going to be negative too.

Vikash Ranjan · Answer

Yeah, indeed she is my bar. It is called aquatics gigs, You know, as being the fund. Um, off course to t done that. People still to cause minus one. Oh, teacher Less one form to equal stew the whole if replaced e x. Hence we have cause a squad six equals to cause winds plus one upon to No, this people indication minus two because to me, it&#x27;s one. Now this is equal to for the ladies. Oh, indeed. Sign two x two Plus It&#x27;s is minus five to pop their ponies. Half really do sign Dubai upon to last five minus sign minus two by upon to minus five. Now this people&#x27;s two off. This is zero. So it is part financed. This is zero. So plus, by way tend to find upon to pull this Cassis each other Finally, densities

Problem

Require the use of various trigonometric identiti…

Problem 56 Easy Difficulty

Evaluate the integrals.
$\int_{-\pi / 2}^{\pi / 2} \cos x \cos 7 x d x$

Answer

0

Related Courses

Thomas Calculus

Related Topics

Discussion

Top Calculus 2 / BC Educators

Anna Marie V.

Samuel H.

Michael J.

Joseph L.

Calculus 2 / BC Courses

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 8

Video Transcript

George B. Thomas Jr.

Thomas Calculus

Anna Marie V.

Samuel H.

Michael J.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

Additional Mathematics Questions

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

0

Thomas Calculus

Anna Marie V.

Samuel H.

Michael J.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

George B. Thomas Jr.Thomas Calculus

Anna Marie V.

Samuel H.

Michael J.

Joseph L.

George B. Thomas Jr.

Thomas Calculus