Question

Evaluate the definite integral.

6 to 4 (3x2−4x+5)dx

hi guys i need help ?

Answer 1

do you know how to integrate polynomials?

Answer 2

i tried but i could not solve this problem

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

its a definite integral so no plus c stuff

Answer 7

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'

Answer 8

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

Answer 9

sorry i meant evaluated at 4 typo

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

it says the answer is incorrect

Answer 15

the answer is 82 or not?

Answer 16

Thanks man for helping me.. it is incorrect.

Answer 17

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

Answer 18

\[6^{3}-2(6)^{2}+5(6)-(4^{3}-2(4)^{2}+5(4))\]
that is the correct one.
you should get 132 i think

Answer 19

it's not correct

Answer 20

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

Answer 21

thanks man

Answer 22

you are welcome. :)