Integrals Analysis: Solving ∫ [-2pi,2pi] (x^2)(sin(e^x))^8 dx

[gutnedawg]

Homework Statement

∫ [-2pi,2pi] (x^2)(sin(e^x))^8 dx <= (16pi^3)/3

Homework Equations

The Attempt at a Solution

I know that the function is almost 0 when x<0 I'm just not sure how to show this mathematically

 

[lanedance]

how about considering the simpler integral first
\int_{-2 \pi}^{2 pi} dx (x^2)

 

[gutnedawg]

how about considering the simpler integral first
\int_{-2 \pi}^{2 pi} dx (x^2)

thanks I was able to figure this out not too long ago.

I just say that x^2 >= the other function and thus ∫ f(x) >= ∫ g(x) on [a,b]
since ∫ x^2 [-2pi,2pi] is equal to (16pi^3)/3 and ∫ f(x) >= ∫ g(x) the inequality holds

thanks though