We have an answer to "Evaluate the integrals. ∫14(v+vv)dv"

chillywilly12a

Answered question

2021-10-24

Evaluate the integrals.

\int_{1}^{4} (\frac{\sqrt{v} + v}{v}) d v

sovienesY

Skilled2021-10-25Added 89 answers

Given:

\int_{1}^{4} (\frac{\sqrt{v} + v}{v}) d v

Explanation:

\int_{1}^{4} (\frac{\sqrt{v} + v}{v}) d v = \int_{1}^{4} (\frac{\sqrt{v}}{v} + \frac{v}{v})

= \int_{1}^{4} (\frac{v^{\frac{1}{2}}}{v} + \frac{v}{v}) d v

= \int_{1}^{4} (v^{\frac{1}{2} - 1} + 1) d v

= \int_{1}^{4} (v^{- \frac{1}{2} + 1}) d v

= {[\frac{v^{\frac{1}{2}}}{\frac{1}{2}} + v]}_{1}^{4}

= {[2 v^{\frac{1}{2}} + v]}_{1}^{4}

= [(2 . {(4)}^{\frac{1}{2}} + 4) - (2 {(1)}^{\frac{1}{2}} + 1)]

= [4 + 4 - 2 + 1]

= 5

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