Integration Problem involving areas under curves

[johno]

Hello all,
I am currently stuck on the following problem:
The diagram shows two regions whose areas are A₁ and A₂. The region whose area is A₁ is bounded by the curve y = (x/a)², x=a and the x-axis. The region whose area is A₂ is bounded by the curve y = (a/x)², x = a, x = b, and the x-axis. If A₂ = 2A₁ and a is not equal to 0, find the ratio of a:b


Where to even begin?
Thanks

 

[Deleted member 4993]

Hello all,
I am currently stuck on the following problem:
The diagram shows two regions whose areas are A₁ and A₂. The region whose area is A₁ is bounded by the curve y = (x/a)², x=a and the x-axis. The region whose area is A₂ is bounded by the curve y = (a/x)², x = a, x = b, and the x-axis. If A₂ = 2A₁ and a is not equal to 0, find the ratio of a:b
View attachment 13243

Where to even begin?
Thanks

A₁ = \(\displaystyle \displaystyle{\int_0^a \left (\dfrac{x}{a}\right )^2 dx}\)

A₂ = ??