Integrating Sinx/x^2 from Y=4 to Y=0 with x=2 and x=√y

[theaviator]

Y=4 x=2
∫ ∫ Sinx ∕ x^2 dx dy
Y=0 x=√y

 

[Astronuc]

Can one find an integral table with

$$\int \frac{sin\,x}{x^2}\,dx$$ ?

Alternatively, expand sin x as an infinite series, divide by x² and solve for each term.

 

[theaviator]

i changed the order of the integration...the final answer i had is the same one in the sheet from which i get the problem...but i don't know id the way i solved it is right or wrong...please HELP...
X=2 y=x^2
∫ ∫ sinx/x^2 dx dy
X=0 y=0

X=2 y=x^2
= ∫ [(sinx/x^2)y] dx
X=0 y=0

X=2
=∫ sinx dx
X=0
X=2
= [ -cosx]
X=0

= -cos2+cos(0)= 1-cos2

 

[nicksauce]

That is correct.