"Evaluate the following definite integral. ∫133x3+2xdx" was answered by our community

Josalynn

Answered question

2021-10-05

Evaluate the following definite integral.

\int_{1}^{3} \frac{3}{x^{3}} + 2 x d x

Brittany Patton

Skilled2021-10-06Added 100 answers

Step 1

\int_{1}^{3} (\frac{3}{x^{3}} + 2 x) d x

Step 2
Using the integral to solve the above integral:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + c

\int_{a}^{b} f (x) d x = {[F (x)]}_{a}^{b} = F (b) - F (b), F (x)

is the integration of f(x)
Step 3

\int_{1}^{3} (\frac{3}{x^{3}} + 2 x) d x = {[3 (\frac{- 1}{2 x^{2}}) + \frac{2 x^{2}}{2}]}_{1}^{3}

= {[\frac{- 3}{2 x^{2}} + x^{2}]}_{1}^{3}

= (\frac{- 3}{2 {(3)}^{2}} + {(3)}^{2}) - (\frac{- 3}{2 {(1)}^{2}} + {(1)}^{2})

= (\frac{- 3}{18} + 9) - (\frac{- 3}{2} + 1)

= \frac{56}{6}

= \frac{28}{3}

Jeffrey Jordon

Expert2021-11-08Added 2605 answers

Answer is given below (on video)

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