U Substitution Video: Sine on the TI-89

U Substitution Sine on the TI-89: Raw Transcript

Hello everyone, Tom from everystepcalculus.com and everystepphysics.com, Iím going to do a U substitution problem that a customer sent me regarding sine and letís get started.
Index 7 to get to both menus, both programs are installed and weíre going to go to U substitution in the menu, we are going to enter our function, we have to pres alpha before we enter anything into this entry lines, alpha square root of X times sine of X to the three halves minus one. I always show you what you have entered, here we have square root of X times sine of X to the three halves minus one, notice the parenthesis, you have to use good parenthesis in math, learn that, itís important and I say itís OK, Iíll give you a chance to change it and when weíre evaluating this we rewrite it because this over here, the square root of X over here matches what weíre going to do in the next screen. U we chose is X to the three halves minus 1, the derivative of that is three halves square root of X and we always take the *** from this side and put it over to di divide by three halves, notice when youíre dividing by three halves youíre going to invert that to two thirds, always remember that important step in algebra and math and here is the same, we wrote it over here so we know itís a U substitution problem, if that wasnít the same and you canít make it to be the same then thatís not a U substitution problem and so here is sine of U is equal to sin of this right here which we know and ** with the integral of the sine of U we have du divided by three halves, here we convert it, two third times the integral of U, two third times the derivative of the integral of the sign of U is minus cosine of U plus C, answer is minus two third cosine of this as we substitute back in for U, pretty neat, everystepcalculus.com or everystepphysics.com, go to my site, buy my programs and pass your calculus class.