Question

Picture inside, but how does one prove an integral to be true without computing.

Answer 1

think about it
what is the maximum value of cosx ?

Answer 2

1

Answer 3

good so in fact
integral of x^2cos(x) <= x^2

Answer 4

do you understand ?

Answer 5

no, I'm suppose to prove the integral is equal to \[\frac{ 1 }{ 3 }\]

Answer 6

wouldn't that equal to 1?

Answer 7

that is right..
but if you understand that
integral of x^2cos(x) <= integral of x^2
the answer is trivial since
integral of x^2 is x^3 / 3
substituting the limits will give you 1/3

Answer 8

integral of x^2cos(x) <= integral of x^2
this statement is true since cos(x) <= 1

Answer 9

but the integral of x^2cos(x) would be x^3/3 -sin(x)

Answer 10

they dont want you to evaluate x^2cos(x) they want you to bound it by an upper limit

Answer 11

and since x^2cos(x) <= x^2
we get what they want

Answer 12

do you understand what i mean ?

Answer 13

@Coolsector I'm trying to, sorry for taking awhile, I'm trying to reread it until I do

Answer 14

you managed to do it ?