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

Question

anonymous · Answer

attachment

anonymous · Answer

think about it
what is the maximum value of cosx ?

anonymous · Answer

1

anonymous · Answer

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

anonymous · Answer

do you understand ?

anonymous · Answer

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

anonymous · Answer

wouldn't that equal to 1?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

do you understand what i mean ?

anonymous · Answer

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

anonymous · Answer

you managed to do it ?