Integrate Initial Acceptance with airSlate SignNow

Integrate initial deal

all right this last exercise is not super deep frankly it's more of algebra exercise frequently these are called initial value problems and the idea is this you're going to be given a derivative function in each like in any such a problem like okay here's the derivative now you know that if you have the derivative function you can find the original function by computing the anti derivative take the antiderivative of the derivative you'll get back the original function but you also know that when you go from a derivative to the original function when you compute an antiderivative you get a plus C where that C could be anything in general well one of the aspects of these initial value problems is that you are going to be given some value from that original function because you see if you not only know what the derivative is but you know something about the original function when you take the antiderivative and you get that C the big thing you know about the original function is going to allow you to find and see exactly which is then going to allow you to know your original function exactly and that's a problem so here's the situation imagine were given this derivative we know that G prime is 7x squared minus 8x cubed plus 5 we want to find G well first off you know the form that G takes take the antiderivative X to the seventh - that's going to be 2x to the fourth plus 5x plus C you know that G of X is going to take that form but here's the thing we're not just wanting to find G of X in general at the scene no we're gonna find it actually what see it and here's how because we know that G not G prime of G of minus 1 is 10 so that says when you plug in minus 1 you get out of 10 so first plug in minus 1 minus 1 to the 7th minus 2 to the minus 1 to the 4th plus 5 minus 1 plus C well since plugging in 1 gives you out 10 you know that this thing is gonna give you out 10 but now check that out there's a bunch of numbers there's only one Leonard the only letter is C CD become so we've got minus 1 to the 7th negative 1 times itself 7 x is minus 1 making it one time itself 4 times a positive 1 so that times minus 2 is just gonna be minus 2 5 times of minus 1 is just a minus 5 plus C is 10 you can see from this s EE what the letter C is what - three - but that's all - ain't adding to both sides C is 18 now knowing what C is we have found our G because we knew our G was of the form X to...