Solved: "Evaluate the following integral. ∫01t52(t−3t)dt"

Tobias Ali

Answered question

2021-05-18

Evaluate the following integral.

\int_{0}^{1} t^{\frac{5}{2}} (\sqrt{t} - 3 t) d t

Alara Mccarthy

Skilled2021-05-19Added 85 answers

Step 1
Given:

\int_{0}^{1} t^{\frac{5}{2}} (\sqrt{t} - 3 t) d t

Step 2

\int_{0}^{1} t^{\frac{5}{2}} (\sqrt{t} - 3 t) d t = \int_{0}^{1} (t^{3} - 3 t^{\frac{7}{2}}) d t

= [\frac{t^{4}}{4} - 6 \frac{t^{\frac{9}{2}}}{9}]_{0}^{1}

= [\frac{t^{4}}{4} - \frac{2 t^{\frac{9}{2}}}{3}]_{0}^{1}

= [\frac{(1)^{4}}{4} - \frac{2 (1)^{\frac{9}{2}}}{3}] - [\frac{(0)^{4}}{4} - \frac{2 (0)^{\frac{9}{2}}}{3}]

= \frac{1}{4} - \frac{2}{3} - (0)

= \frac{- 5}{12}

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