Antiderivative Calculator

Hello again everyone, this is Tom from everystepcalculus.com, everystepphysics.com, I’m gonna show you how to turn your titanium calculator with my programs into a antiderivative calculator. Okay, so, index 8 to get to my menu. I’m gonna do a U substitution, because most problems are U substitution integration and antiderivative is really doing the integral of a derivative. Where as an integral itself is doing an integral of a function which might be a derivative or not. But antiderivative is really an integral, and it’s an indefinite integral because you have to have a plus C at the end and somebody has to decide on the C, there’s 10 million integrals for an indefinite integral, all decided by what the plus C is. Who decides that, I have no idea. U substitution, enter a function, you have to press alpha before you enter anything into these entry lines here, don’t forget that. Alpha and the square root second square root. And the square root of 6 times X minus 1. Close off the parenthesis. Oh, didn’t press alpha I guess. 6 times x minus 1. That’s better. Now we show you what you’ve entered, you can change it if you want. Say it’s okay. And we’re into the problem. U is whatever’s in the parenthesis, you should be able to do the derivative of whatever’s in here in a second okay, in your sleep– for instance, the derivative of 6x is 6. Well here you have U of 6x minus 1, and the derivative is 6dx. We want to always have the dx by itself, because the dx is by itself up here, right. So you’re gonna take this and use algebra, and bring it over to the other side, and divide du by 6. That equals (1)dx over here. So now, the square root of u then is equal to the square root of 6x minus 1 because we made this u. So that equals the integral of u to the one half, because if this was a cube root it would be one third, if this was the fifth root it’d be one fifth here. But this is the square root, so it’s the one half. And then you have to add the du divided by 6, which we formulated before. That’s one of the big tricks in u substitution that took me 10 years to figure it out. So we have to bring all constants out of the integral, which we do here, one sixth here, we add 1 to the 1/2 here, which becomes 3, 3 halves, divided by 3 halves, so you have one sixth when you divide by a fraction, you invert multiply, so we inverted the fraction. Two thirds. And the answer’s 1/9th, 6 to that. Pretty neat, huh? Everystepcalculus.com, go to my site, buy my program if you want to pass calculus and do your homework. Have a good one!