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OpenStudy (anonymous):

Evaluate the definite integral. 6 to 4 (3x2−4x+5)dx hi guys i need help ?

OpenStudy (anonymous):

do you know how to integrate polynomials?

OpenStudy (anonymous):

i tried but i could not solve this problem

OpenStudy (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

OpenStudy (anonymous):

then by applying newton's Newton leibniz you would plug in 4 and 6 to solve.

OpenStudy (anonymous):

=(x^3 - 2x^2 +5x) then evaluate it at 6 then subtract (x^3 - 2x^2 +5x) evaluated at 5

OpenStudy (anonymous):

its a definite integral so no plus c stuff

OpenStudy (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'

OpenStudy (anonymous):

\[\int\limits_{4}^{6}3x ^{2}-4x +5 dx = [x ^{3}-2x ^{2}+5x ] |_{4}^{6}\]

OpenStudy (anonymous):

sorry i meant evaluated at 4 typo

OpenStudy (anonymous):

\[\int\limits_{4}^{6} (3x^2-4x+5)dx\]

OpenStudy (anonymous):

\[6^3 -4(6) + 5(6) -(4^3 -4(4) +5(4))\]

OpenStudy (anonymous):

smart, are you still confused? it is pretty straight forward from here. nosmada has explained it just now too.

OpenStudy (anonymous):

\[6^3−4(6)^2+5(6)−(4^3−4(4)^2+5(4)) \] sorry disregard that last one

OpenStudy (anonymous):

it says the answer is incorrect

OpenStudy (anonymous):

the answer is 82 or not?

OpenStudy (anonymous):

Thanks man for helping me.. it is incorrect.

OpenStudy (anonymous):

no wiat you have to evaluate the polynomial I posted. the one nmosmada posted is incorrect. use mine and solve.

OpenStudy (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

OpenStudy (anonymous):

it's not correct

OpenStudy (anonymous):

oh well, too bad. I did the procedure correctly. maybe your book has an error in it.

OpenStudy (anonymous):

thanks man

OpenStudy (anonymous):

you are welcome. :)

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