What is the integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2} ?

The integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2} is 22/3

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integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2}

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} + \frac{1}{2} y^{- \frac{1}{2}} d y

\frac{22}{3}

Decimal Notation

7.33333 \dots

Solution steps

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} + \frac{1}{2} y^{- \frac{1}{2}} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} d y + \int_{4}^{9} \frac{1}{2} y^{- \frac{1}{2}} d y

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} d y = \frac{19}{3}

\int_{4}^{9} \frac{1}{2} y^{- \frac{1}{2}} d y = 1

= \frac{19}{3} + 1

Simplify

\frac{19}{3} + 1 : \frac{22}{3}

= \frac{22}{3}

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What is the integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2} ?
The integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2} is 22/3