APFIVE Evaluating an Integral for Total Accumulation
A tank is filled with water at a varying rate given by $$R(t)=\frac{5*\sqrt{t}+3}{t^{1/3}}$$ (liters/minute) for t > 0. Estimate the total volume added from t = 1 to t = 8 minutes by evaluating $$\int_{1}^{8} R(t) dt.$$ Express your answer exactly.
A
$$\frac{480*\sqrt{2}+129}{14}$$
B
$$\frac{480*\sqrt{2}+130}{14}$$
C
$$\frac{480*\sqrt{2}+129}{7}$$
D
$$\frac{480*\sqrt{2}+129}{14} + \ln(2)$$
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