anonymous
  • anonymous
Evaluate the definite integral. 6 to 4 (3x2−4x+5)dx hi guys i need help ?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
do you know how to integrate polynomials?
anonymous
  • anonymous
i tried but i could not solve this problem
anonymous
  • anonymous
Possible intermediate steps: integral (5-4 x+3 x^2) dx Integrate the sum term by term and factor out constants: = 3 integral x^2 dx+ integral 5 dx-4 integral x dx The integral of x^2 is x^3/3: = x^3+ integral 5 dx-4 integral x dx The integral of x is x^2/2: = x^3-2 x^2+ integral 5 dx The integral of 5 is 5 x: = x^3-2 x^2+5 x+constant

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anonymous
  • anonymous
then by applying newton's Newton leibniz you would plug in 4 and 6 to solve.
anonymous
  • anonymous
=(x^3 - 2x^2 +5x) then evaluate it at 6 then subtract (x^3 - 2x^2 +5x) evaluated at 5
anonymous
  • anonymous
its a definite integral so no plus c stuff
anonymous
  • anonymous
Take the indefinite integrate of each individual term using the laws of integration. Next, evalute your answer at each endpoint..then subtract your evaluation at 'a' from your evaluation at 'b'
anonymous
  • anonymous
\[\int\limits_{4}^{6}3x ^{2}-4x +5 dx = [x ^{3}-2x ^{2}+5x ] |_{4}^{6}\]
anonymous
  • anonymous
sorry i meant evaluated at 4 typo
anonymous
  • anonymous
\[\int\limits_{4}^{6} (3x^2-4x+5)dx\]
anonymous
  • anonymous
\[6^3 -4(6) + 5(6) -(4^3 -4(4) +5(4))\]
anonymous
  • anonymous
smart, are you still confused? it is pretty straight forward from here. nosmada has explained it just now too.
anonymous
  • anonymous
\[6^3−4(6)^2+5(6)−(4^3−4(4)^2+5(4)) \] sorry disregard that last one
anonymous
  • anonymous
it says the answer is incorrect
anonymous
  • anonymous
the answer is 82 or not?
anonymous
  • anonymous
Thanks man for helping me.. it is incorrect.
anonymous
  • anonymous
no wiat you have to evaluate the polynomial I posted. the one nmosmada posted is incorrect. use mine and solve.
anonymous
  • anonymous
\[6^{3}-2(6)^{2}+5(6)-(4^{3}-2(4)^{2}+5(4))\] that is the correct one. you should get 132 i think
anonymous
  • anonymous
it's not correct
anonymous
  • anonymous
oh well, too bad. I did the procedure correctly. maybe your book has an error in it.
anonymous
  • anonymous
thanks man
anonymous
  • anonymous
you are welcome. :)

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