Answer:
Step-by-step explanation:
Root:
n≈0.00833333 m + 0.666667
Root for the variable n:
n≈-0.0833333 (-0.1 m - 8)
Derivative:
d/dm(0.1 m + 8 - 12 n) = 0.1
Indefinite integral:
integral(8 + 0.1 m - 12 n) dm = 0.05 m^2 - 12 m n + 8 m + constant
Definite integral over a disk of radius R:
integral integral_(m^2 + n^2<R^2)(0.1 m - 12 n + 8) dm dn = 8 π R^2 + 0
Definite integral over a square of edge length 2 L:
integral_(-L)^L integral_(-L)^L (8 + 0.1 m - 12 n) dn dm = 32 L^2 + 0
