Find positive numbers a and b so that the change of variables s=ax, t=by transforms the integral ∫∫rdxdy into ∫∫t∣∣∣∂(x, y)∂(s, t)∣∣∣dsdt for the region r, the rectangle 0≤x≤15, 0≤y≤60 and the region t, the square 0≤s, t≤1. a= b= what is ∣∣∂(x, y)∂(s, t)∣∣ in this case? ∣∣∂(x, y)∂(s, t)∣∣=

S = ax
It is required to find the value of a which make:
0 ≤ s ≤ 1 when 0 ≤ x ≤ 15
∴ s = 0 when x = 0     ⇒⇒⇒ a = 0 (unacceptable)
or s = 1 when x = 15  ⇒⇒⇒ a = s/x = 1/15

Similarly, t = by
It is required to find the value of b which make:
0 ≤ t ≤ 1 when 0 ≤ y ≤ 60
∴ t = 0 when y = 0     ⇒⇒⇒ b = 0 (unacceptable)
or t = 1 when y = 60  ⇒⇒⇒ b = t/y = 1/60



∴ x = 15s  and  y = 60t



Note: it is not matrix it is determinant

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