What is the integral from 3 to 5 of (y^2)/2+1/(2y^2) ?

The integral from 3 to 5 of (y^2)/2+1/(2y^2) is 82/5

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integral from 3 to 5 of (y^2)/2+1/(2y^2)

\int_{3}^{5} \frac{y ^{2}}{2} + \frac{1}{2 y ^{2}} d y

\frac{82}{5}

Decimal Notation

16.4

Solution steps

\int_{3}^{5} \frac{y ^{2}}{2} + \frac{1}{2 y ^{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_{3}^{5} \frac{y ^{2}}{2} d y + \int_{3}^{5} \frac{1}{2 y ^{2}} d y

\int_{3}^{5} \frac{y ^{2}}{2} d y = \frac{49}{3}

\int_{3}^{5} \frac{1}{2 y ^{2}} d y = \frac{1}{15}

= \frac{49}{3} + \frac{1}{15}

Simplify

\frac{49}{3} + \frac{1}{15} : \frac{82}{5}

= \frac{82}{5}

\int x^{3} - 3 x^{- 4} - 2 d x

\int x^{2} lo g_{e} (x) d x

\frac{d y}{d t} = y + 1

\int_{0}^{7} 49 - x^{2} d x

\frac{\partial}{\partial x} ((x - 2) (1 - e^{- x}))

What is the integral from 3 to 5 of (y^2)/2+1/(2y^2) ?
The integral from 3 to 5 of (y^2)/2+1/(2y^2) is 82/5