Question

Why is integral of y = x^2 + b , 1/3 x^3 + b but integral of y = x + b is 1/2 x^2 + x ?
sorry if my question is simple or incorrect :) i'm new at calculus :)

Answer 1

is b a constant?

Answer 2

yes :)

Answer 3

Hey... uhh
\[\Large \int (x^2+b)dx = \frac13x^3 + bx \color{orange}{+C}\]

Answer 4

Wrong emphasis.. I should have emphasised the bx part.

Answer 5

sorry i don't understand :)

Answer 6

Well the integral of a constant is just THAT constant times x.

So the integral of the b part is bx, not simply b.

Answer 7

take the derivative of your answer if it doesnt give you what you integrated then you did it wrong

Answer 8

Actually^ LOL

Answer 9

Im so rusty with integrals blah I need to relearn them they are a lot of fun

Answer 10

so my question is wrong?

Answer 11

what is the derivative of 1/3 x^3 + b

Answer 12

also you didnt include + c so you were wrong even if your answer was right

Answer 13

i think it's x+b ?

Answer 14

perhaps i made mistake

Answer 15

someone is going to have to go over this with him I'm too rusty and have a journal to read on some journal article on some histone demethylation protein that is in rice that I'm suppose to care about

Answer 16

Okay... let's recap:
\[\Large \int(x^2+b)dx\]

Answer 17

You know that antidifferentiation (integration) is linear, so we can distribute it:
\[\Large = \int x^2dx + \int b dx\]
Right?

Answer 18

Now all you need to recall is the power rule for integration...
\[\Large \int ax^ndx = \frac{ax^{n+1}}{n+1}\color{orange}{+C} \qquad n \ne -1\]

Answer 19

no, i think i should learn more

Answer 20

Not forgetting of course, that \[\Large b = bx^0\]

Answer 21

sorry wait for about...some days i think i have to learn more,and ask some questions :)

Answer 22

i'll keep this question open