calculate-0-1-t-2-1-t-3-dt-

Question Number 53782 by maxmathsup by imad last updated on 25/Jan/19

c a l c u l a t e \int_{0}^{1} \frac{t^{2}}{1 + t^{3}} d t

Answered by Smail last updated on 26/Jan/19

\int_{0}^{1} \frac{t^{2}}{1 + t^{3}} d t = \frac{1}{3} \int_{0}^{1} \frac{d (1 + t^{3})}{1 + t^{3}} = \frac{1}{3} {[l n ∣ 1 + t^{3} ∣]}_{0}^{1}

= \frac{l n 2}{3}

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