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125=\int_{0}^{T} 75-3 \mathrm{t}^{2} \mathrm{dt}=75 \mathrm{t}-\left.\mathrm{t}^{3}\right|_{0} ^{\mathrm{T}}=75 \mathrm{~T}-\mathrm{T}^{3} \text { so } \mathrm{T}^{3}-75 \mathrm{~T}+125=0