Don't try to compute it!

Calculus Level 5

Compute the following integral

$M=\displaystyle \int_{0}^{1} \dfrac{\sin(2x)}{x}~\Bbb{d}x+\int_{0}^{2} \ln(x)\cos(x)~\Bbb{d}x$

Input your answer as $\lfloor 100M\rfloor$

You may only use functions available on a standard scientific calculator.

The answer is 63.

2 solutions

Trevor Arashiro
Apr 9, 2017

If we integrate the first integral by parts, we get

$\ln(2x)\sin(2x)\displaystyle |_0^1-\int_{0}^{1} 2\ln(2x)\cos(2x)~\Bbb{d}x+\int_{0}^{2} \ln(x)\cos(x)~\Bbb{d}x$

Note that the first and second integrals now cancel. Evaluating the left most term of the equation above we get $\ln(2)\sin(2)-0\approx \boxed{0.63}$

Hey, Trevor! Long time no talk. How's it going?

Quite the Masters, huh!? I really like Rose, but I was pulling for Garcia all the way; he was so deserving of finally winning a major, and it was fitting that he had to overcome so much adversity to do so. The fact that Dustin Johnson couldn't compete, (he's such an idiot sometimes), doesn't diminish the victory at all, which I was worried might happen when the tournament began. The next person I hope to see finally win a major is Fowler.

Brian Charlesworth - 4 years, 2 months ago

Hello! Long time no talk indeed. I've been chilling pretty hard, 7 weeks left in school and I'm just having fun. I love my classes right now and can't wait till college. How bout you?

Oh my gosh this was the most exciting masters in a while! The emotional roller coaster, the continuous fight for the lead between Garcia and Rose, and the heart breaking misses on 18. I was pulling for Garcia as well, he's deserved a major title for quite a while now. However,the victory was somewhat bitter sweet as I have been a J Rose fan my entire life... simply because I played as him in my 2007 EA Sports Tiger Woods PGA game, lol. Kuchar didn't leave himself out of the headlines, making a nice hole in one and giving the ball to a 10 year old kid in the stands. Gotta love that guy.

Trevor Arashiro - 4 years, 2 months ago

I'm doing well, thanks. Almost done with high school, huh? Glad you're chillin' like a villain and looking forward to your future. Are you headed to the mainland for college or staying in Paradise?

That's funny about the way you became a JR fan. He, Kuchar and Jason Day are probably the three classiest guys on the tour. That kid in the orange shirt will be a Kuchar (and golf) fan for life now. I noticed too that Matt was waiting in line to congratulate Garcia as he and his fiancee walked to the clubhouse, (or Butler Cabin, not sure). It's amazing how the Masters, of all the majors, almost always produces the best storylines, and this year's was a classic. I'm hoping Rose wins the British this year; that would be poetic justice.

Brian Charlesworth - 4 years, 2 months ago

@Brian Charlesworth – I'm going to Carnegie Mellon School of Computer Science. I almost went to Upenn Wharton but my passions changed from Business to CS between the beginning of senior year and College Decisions.

Garcia has completely changed as a person over the past decade. I always thought of him as the cocky guy who mouthed off in front of Tiger. Despite not having won a single major, he used to insist that he could beat Tiger any day. It would be very poetic if Rose won the British Open, and I don't think it's too far fetched. And just to add one, I don't think a list of the most courteous golfers would be complete without Davis Love III.

Trevor Arashiro - 4 years, 2 months ago

@Trevor Arashiro – Great choice of discipline and school! CMU ranks right alongside MIT and Stanford, so congrats on being accepted there! Pittsburgh will be quite the change from Hawaii, but I'm sure you'll make the adjustment in no time. :)

Yeah, Garcia has certainly matured for the better. I've grown to like the guy, recognizing that he was doing his best to battle with his demons. It sounds like his fiancee has made a big difference in his attitude. To hear the crowd pulling for him on Sunday will have done him almost as much good as the win itself. I would expect to see him win another major in the future, likely the British. And 3D is indeed a classy guy, but honestly, the golf world is full of good guys. Nicklaus is still my all-time fave in every way, though.

Brian Charlesworth - 4 years, 2 months ago

Dangerous looking simple problem. Nicely done +1!

Prakhar Bindal - 4 years, 2 months ago

I seems obvious that the two rightmost terms are equal (considering the bounds) but couldn't see it mathematically if they really are bound to be..(equal)

Vishal Yadav - 4 years, 2 months ago

Anand Raj
Apr 11, 2017

Substitute 2x = t in first integral and then integrate it by parts taking Sin(2x) as I function and 1/x as second function.... Easy as Hell!! 😑 Not a Level 4 Question!!

Don't try to compute it!

The answer is 63.

2 solutions

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