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Hi there!
A)
We can evaluate an integral to solve:
[tex]\int\limits^{10}_0 {2 + 0.4t^{2}} \, dt = 2(10) + 4/30(1000) = 153.333 L[/tex]
B)
Use the FTC to solve:
F(0) - ∫(0 to x min)f(t) = F(x) = 0
[tex]75 - \int\limits^{t}_0 {2 + 0.4t^2} \, dt = 0[/tex]
Solve:
[tex]75 = \int\limits^{t}_0 {2 + 0.4t^2} \, dt[/tex]
Evaluate:
[tex]75 = 2t + 4/30t^{3}[/tex]
Use a graphing utility to solve:
t = 7.65 min
C)
Use the slope formula to find the AROC:
f(10) - f(0) / 10 - 0 = 42 - 2 / 10 - 0 = 4 L/m²