TheLonelyDog Posted February 2, 2015 Report Share Posted February 2, 2015 Hello! I'm having a bit of a problem with solving this integral by hand. Can someone help me solve it? I tried using substitution, but I can't get rid of the arctan(x/25). Thanks! Reply Link to post Share on other sites More sharing options...
Vioh Posted February 3, 2015 Report Share Posted February 3, 2015 Hello! I'm having a bit of a problem with solving this integral by hand. Can someone help me solve it? I tried using substitution, but I can't get rid of the arctan(x/25). Thanks! I've tried to do this question many times, but unfortunately I can't come up with a good way of solving it by hand. My attempt was to use integration by parts, differentiating the arctan, while integrating the square root. The differentiation comes out really nicely, because d/dx (arctan(x/25)) = 25/(625+x^2), which I can imagine to be nicely simplified with the square root. But I couldn't integrate the square root; trigonometric substitution couldn't help me here, because the result was so complicated that I couldn't bother to continue. I guess there are probably many other integration tricks/methods to solve this question by hand, but those methods would be way beyond the IB scope. But then I begin to wonder, why do you have to solve it by hand anyway? Is there any particular reason? Because it takes like 5 seconds to solve this question using a GDC, especially as the integral is definite. 1 Reply Link to post Share on other sites More sharing options...
TheLonelyDog Posted February 3, 2015 Author Report Share Posted February 3, 2015 (edited) I've tried to do this question many times, but unfortunately I can't come up with a good way of solving it by hand. My attempt was to use integration by parts, differentiating the arctan, while integrating the square root. The differentiation comes out really nicely, because d/dx (arctan(x/25)) = 25/(625+x^2), which I can imagine to be nicely simplified with the square root. But I couldn't integrate the square root; trigonometric substitution couldn't help me here, because the result was so complicated that I couldn't bother to continue. I guess there are probably many other integration tricks/methods to solve this question by hand, but those methods would be way beyond the IB scope. But then I begin to wonder, why do you have to solve it by hand anyway? Is there any particular reason? Because it takes like 5 seconds to solve this question using a GDC, especially as the integral is definite. Well, it's the formula for the surface area of the shape formed by rotating the curve 15.537*arctan(x/25) around the x=axis. I am using it in my Math HL IA, and my teacher recommended that anything done in the IA should be done by hand. I also tried al night to solve it, no luck. I'll probably just use the GDC and hope the IA won't get downgraded because of this. Edited February 3, 2015 by abaaaabbbb63 Reply Link to post Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.