<p>How would you integrate sin((pi*e^x)/2)?
It seems like Calculus AB can't answer this...</p>
<p>well u can just go straight out and do it since the deriv of e to the x is e to the x. </p>
<p>the answer is</p>
<p>(-2/pie)cos(pie times e to the x over 2) differentiate to verify that it works</p>
<p>That problem is beyond calculus AB or BC. You can try u = pi/2*e^x but you'll get the integral of sin(u)/u, which doesn't have a closed form solution (it actually has a name: the "sine integral"). The definite integral from -inf to inf of your function would be pi/2.</p>
<p>Any calculus experts here have better info?</p>
<p>I dont think thats the right answer kungfumaster cause I tried many different versions of u substitution...</p>
<p>oh right! chain rule! haha</p>
<p>oh ok</p>
<p>i'm too lazy to solve. but you need to do integration by parts.
look it up on internet or textbook.</p>
<p>nope, integration by parts doesn't work either - I tried that long time ago</p>
<p>Isn't integration by parts for multiplication? That wouldn't apply here.</p>
<p>u= pi/2 * e^x
du = same</p>
<p>sin(u) --> -cos(u)/du = -cos(pi/2 *e^x)/(pi/2 *e^x) + C</p>
<p>If you take the derivative to check, it should be</p>
<p>sin(pi/2 *e^x) * (pi/2 *e^x)/(pi/2 *e^x) = sin(pi/2 *e^x)</p>
<p>I think that's right (hopefully)</p>
<p>ThisCouldBeHeavn's answer is not correct because to take the derivative to check, you need to use either the quotient rule or the product rule:</p>
<p>fg'+f'g</p>
<p>(-cos(pi/2 *e^x))(-((pi/2 *e^x)^-2)(pi/2 *e^x)) + (sin(pi/2 *e^x)(pi/2 *e^x))((pi/2 *e^x)^-1)</p>
<p>...which does not check out right. Have you learned sequences and series yet? You might try using that because I don't think regular integration works here.</p>
<p>Regular intergration does not on this problem and like nicole said you would need to use sequences and series to evaulate it as an infinite series.</p>
<p>I know you would need to use series for sin(x^2), sin(e^x), cos(e^x) so even adding a constant (pi/2) would know change the problem to make it solvable using intergration by parts or by subsitution.</p>
<p>I tried to change the sin(pi*e^x/2) to a different form without using series and it doesn't work.</p>
<p>Looks like it's beyond the AP curriculum as someone said ---- I do not remember learning "sine integral" or "Si(x)"</p>
<p>I used the Wolfram Mathworld Integrator and the answer is "Si(e^x*pi/2)" </p>
<p>It says Si(z) is defined as Integral(sin(x)/x, x, 0, z) (z being a complex number).</p>
<p>wow...what math class are you in?</p>
<p>Yes, Wolfram is right, that is the sine integral. Again, this is beyond AP, there is no closed form solution. I.e., to write the solution out, you have to use an infinite series.Since the integral reduces to sin(u)/u, using u=pi/2*e^x, you just need the expansion for sin(u), divided by u.</p>
<p>Shouldn't you guys be taking a little break on this stuff? :)</p>