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/sci/ - Science & Math

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2743335 No.2743335 [Reply] [Original]

Alright, /sci/, you'll probably hate me for asking this, and i hate myself for not knowing it on the spot, but this is really bugging me right now...

what is the anti-derivative of: (SqRoot X)dx/-2?

Thanks in advance

>> No.2743359
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2743359

>anti-derivative

>> No.2743370

-(x*x^0.5)/2

>> No.2743379

>>2743359

unused term, but correct

OP, rewrite that because I cant see shit

>> No.2743402

-x^(2/3)/3 +C
that is assuming the original function was -sqrt(x)/2

>> No.2743418

>>2743402

You meant to write x^(3/2) there.

>> No.2743445

-1/2 * x^1/2

-1/2 * 2/3 * x^(3/2)

>> No.2743451

>>2743379
ok, let me make this easier:
I was stuck doing a substitution, the original problem stated:

Int: X[SqRoot(1-X^2)]dx

>> No.2743469

>>2743451
Let u = 1 - x^2
du = -2x dx
(-1/2)du = x dx

original x * (1 - x^2)^(1/2)dx
substitute in u du. x dx is canceled.
(-1/2) * u^(1/2) du.
(-1/2) * (2/3) * u^(3/2).
(u^(3/2))/3

>> No.2743498

>>2743469
substituting back in
-1/3 * (1 - x^2)^(3/2)