<p>How often do trig integrals do they require you to know the complicated trig identities on top of your head?</p>
<p>I’ve seen them on AB questions, so I’m assuming they appear on BC as well.</p>
<p>They aren’t that complicated. :p</p>
<p>Trig-substitution isn’t tested on the exam. There is a list of common trig integrals/derivatives that you should know for the exams, you can probably find it online somewhere.</p>
<p>I’ve seen questions where knowing the double angle identities for cos (2theta) come in handy, and where knowing your Pythagorean identities are helpful. I have yet to see any questions where you are required to know your sum or difference identities or your half-angle identities.</p>
<p>I meant subbing trig identities and then use u-substitution .</p>
<p>Subbing trig identities? Can you give an example?</p>
<p>just know the double and half angle formulas for sin and cos and you’re set for a good amount of trig integrals</p>
<p>Why would you need double or half angle identities for trig integrals? To integrate something like sin(2x), you just use u-substitution. The identities you need to know to integrate trig is power reducing, for something like [cos(x)]^2.</p>
<p>On PR, they have these weird questions</p>
<p>In order to integrate (sin x)^2 dx, you need to use the identity that cos(2x) = 1 - 2(sin x)^2 to rewrite the integral as a function of cos(2x), and then you can integrate the ensuing expression. I guess that’s what I meant by needing to know your double angle identities. :)</p>
<p>^^ exactly ;)</p>
<p>I don’t memorize the power reducing formulas, so I go back to double and half angle formulas.</p>
<p>Aren’t power-reducing formulas easier? There are only 2 formulas as opposed to 4 double-angle identities (1 for sin 2x and 3 for cos 2x). I guess it’s just personal preference.</p>
<p>no matter what kinds of curveballs they threw at me, I found that double/half angle formulas really helped as supposed to memorizing two specific integrals.</p>
<p>I guess you’re right, it’s just personal preference. I don’t memorize any of the derivatives/integrals (except for sin, cos, and e^x). I still find myself using the quotient rule to find the derivative of secant and cosecant and drawing right triangles to do trig integrals. Call me inefficient, but I tend to stay away from memorization when doing calc.</p>