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Find the interval [a,b] for which the value of the integral b
s(2+xx^2)dx
a
is maximum
 one year ago
 one year ago
Find the interval [a,b] for which the value of the integral b s(2+xx^2)dx a is maximum
 one year ago
 one year ago

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UnkleRhaukusBest ResponseYou've already chosen the best response.0
is this your question ?\[\int\limits_a^b(2+xx^2)\text dx\]
 one year ago

jackkim4Best ResponseYou've already chosen the best response.0
yes!!! sry first time here....
 one year ago

jackkim4Best ResponseYou've already chosen the best response.0
is the answer [1, 2] or [1,1/2] ??
 one year ago

helder_edwinBest ResponseYou've already chosen the best response.0
as @UnkleRhaukus pointed out, you have maximize \[ \large F(a,b)=\int_a^b(2+xx^2)\,dx \]
 one year ago

helder_edwinBest ResponseYou've already chosen the best response.0
which one gives u the greatest area?
 one year ago

jackkim4Best ResponseYou've already chosen the best response.0
doesnt [1, 1/2] wait no... it's [1, 2]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
what did you get when you integrated
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\[\int\limits_a^b(2x^0+x^1x^2)\text dx=\frac{2x^1}1+\frac{x^2}2\frac{x^3}{3}\Big_a^b\]\[=2(ba)+\frac{(ba)^2}2\frac{(ba)^3}{3}\] right?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
actually i think i made a mistake
 one year ago

jackkim4Best ResponseYou've already chosen the best response.0
[2b+b^2/2b^3/3][2a+2a^2/2a^3/3]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\[\int\limits_a^b(2x^0+x^1x^2)\text dx=\frac{2x^1}1+\frac{x^2}2\frac{x^3}{3}\Big_a^b\]\[\qquad\qquad=\left({2b}+\frac{b^2}2\frac{b^3}3\right)\left({2a}+\frac{a^2}2\frac{a^3}3\right)\]yeahs
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
so when is this maximum
 one year ago

jackkim4Best ResponseYou've already chosen the best response.0
at a= 1 b= 2 ! right?
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
Maximize F(b) by derivative, minimize F(a) by derivative.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\[=b\left({2}+\frac{b}2\frac{b^2}3\right)+a\left({2}\frac{a}2+\frac{a^2}3\right)\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\[=6b\left(12+3b2b^2\right)+6a\left(2a^23a12\right)\]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
\[\large F \prime (b)=2+bb^2=0\]\[\large \text{max at } b=2\]\[\large F \prime (a)=2+aa^2=0\]\[\large \text{max at } a=1\] interval: [1, 2]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
wow, my answer is among the choices given.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
typo mistake. it should be min at a = 1
 one year ago

jackkim4Best ResponseYou've already chosen the best response.0
yayyyyyy tytytyty! :')
 one year ago
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