Question

Evaluate the following integral. \int_{0}^{1}t^{\frac{5}{2}}(\sqrt{t}-3t)dt

Applications of integrals
ANSWERED
asked 2021-05-18
Evaluate the following integral.
\(\int_{0}^{1}t^{\frac{5}{2}}(\sqrt{t}-3t)dt\)

Answers (1)

2021-05-19
Step 1
Given:
\(\int_{0}^{1}t^{\frac{5}{2}}(\sqrt{t}-3t)dt\)
Step 2
\(\int_{0}^{1}t^{\frac{5}{2}}(\sqrt{t}-3t)dt=\int_{0}^{1}(t^{3}-3t^{\frac{7}{2}})dt\)
\(=[\frac{t^{4}}{4}-6\frac{t^{\frac{9}{2}}}{9}]_{0}^{1}\)
\(=[\frac{t^{4}}{4}-\frac{2t^{\frac{9}{2}}}{3}]_{0}^{1}\)
\(=[\frac{(1)^{4}}{4}-\frac{2(1)^{\frac{9}{2}}}{3}]-[\frac{(0)^{4}}{4}-\frac{2(0)^{\frac{9}{2}}}{3}]\)
\(=\frac{1}{4}-\frac{2}{3}-(0)\)
\(=\frac{-5}{12}\)
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