Question

how do Integral a backwards derivate

Answer 1

der? What?

Answer 2

der = derivatives

Answer 3

So the question is, how come the reverse of an integral is a derivative?

Answer 4

is yes and also how to do this type of problem as well

Answer 5

reverse chain rule

Answer 6

yes that is what i am asking

Answer 7

for instance like
differenitate
\[e^{3x} \left(cosx-3sinx\right) \]
then integrate
\[\int\limits e^{3x}sinxdx \]?

Answer 8

okay but in this form what are keys to know when to use this rule??

Answer 9

So when you use the chain rule you take the exponent and multiply it by it as a coefficient and then subtract the exponent by one. In integration for the chain rule you'll simply be reversing this process exactly.

To do that, add 1 to the exponent, then divide by the new added exponent.

So for example if you want to integrate 3x^2 you would change the exponent to 3 and then divide by 3 to get x^3 as the integral.

Answer 10

I described power rule, not chain rule, sorry.

Answer 11

But you probably need help with that too, so I'll leave it.

Answer 12

asking how to when when to use integration is like asking when to use addition or any other mathematical technique
really vague questions like this are hard to answer, and there are many techniques the the actual act of integration depending on the function you are integrating

Answer 13

I am just trying to get a general idea is all.

Answer 14

I am not in high school, I am a college student here.

Answer 15

general idea... for an xy-rectangular graph the area under a function f(x) from x=a to x=b is\[\int_a^bf(x)dx\]