anonymous
  • anonymous
How do you evalute definite integrals with a radical in it?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
use the exponent form of a square root... ^(1/2)
amistre64
  • amistre64
or..use substitution methods designed for radical problems...
amistre64
  • amistre64
got anything specific?

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anonymous
  • anonymous
its the square root of 36+3x i tried putting 36^1/2 + 3x^1/2 but i get lost on what to do next.
amistre64
  • amistre64
you cant divde addition up into seperate radical parts :)
anonymous
  • anonymous
ohh so you mean i have to put (36+3x)^1/2 and go from there?
amistre64
  • amistre64
\[\sqrt{36 + x} \neq \sqrt{36} + \sqrt{x}\]
amistre64
  • amistre64
yes, thats what I mean :) if we let u = 36+3x then we evaluate u^(1/2) du
amistre64
  • amistre64
u = 36 + 3x du = 3 dx du/3 = dx [S] (36 +3x)^(1/2) dx [S] u^(1/2) du/3
amistre64
  • amistre64
\[\int\limits_{} (36+3x)^{1/2} dx \rightarrow \int\limits_{} \frac{u^{1/2}}{3}du\]
amistre64
  • amistre64
it ate my fraction bar ...lol
amistre64
  • amistre64
any of this make sense?
anonymous
  • anonymous
i follow so far, yes. thank you so much :)
anonymous
  • anonymous
so now, i plug in the two #'s and subtract them from eachother right ?
amistre64
  • amistre64
if it had an interval set; then we integrate this new integral to get the higher function of F(u); then resubstitute back in the "x" parts from the "u" parts to get the F(x) OR... modify the original interval to work for u instead if x :)
anonymous
  • anonymous
what do you mean higher function of F(u)?
amistre64
  • amistre64
\[\frac{1}{3} \int\limits_{a}^{b} u^{1/2}du \rightarrow \frac{1}{3} * \frac{2u^{3/2}}{3} = \frac{2u^{3/2}}{9}|_{u(a)}^{u(b)}\]
amistre64
  • amistre64
F(u) is a function of "u"
amistre64
  • amistre64
we can resubstitute the "value" of u back like this:\[\frac{2u^{3/2}}{9} \rightarrow \frac{2(36+3x)^{3/2}}{9}|_{a}^{b}\]
amistre64
  • amistre64
now it become F(x) since "x" is the variable again.... F(b) - F(a) gets your answer
anonymous
  • anonymous
okay i think i get it now. thank you so much
amistre64
  • amistre64
youre welcome :) it gets better with practice ;)

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