First slide

Evaluation of definite integrals

Question

_{$\int_{0}^{3} x \sqrt{1 + x} d x =$}

Easy

A

_{$\frac{116}{15}$}
B

_{$\frac{15}{116}$}
C

0
D

_{$\frac{115}{16}$}

Solution

Put _{$1 + x = t^{2}$}
_{$d x = 2 t d t$}

_{$\int_{1}^{2} (t^{4} - t^{2}) (2 d t)$}

_{$= 2 {(\frac{t^{5}}{5} - \frac{t^{3}}{3})}_{1}^{2} = \frac{116}{15}$}

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