What is the integral from 1 to 2 of (x^2)/2+1/(2x^2) ?

The integral from 1 to 2 of (x^2)/2+1/(2x^2) is 17/12

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integral from 1 to 2 of (x^2)/2+1/(2x^2)

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

\frac{17}{12}

Decimal Notation

1.41666 \dots

Solution steps

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

Apply the Sum Rule:

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

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

\int_{1}^{2} \frac{x ^{2}}{2} d x = \frac{7}{6}

\int_{1}^{2} \frac{1}{2 x ^{2}} d x = \frac{1}{4}

= \frac{7}{6} + \frac{1}{4}

Simplify

\frac{7}{6} + \frac{1}{4} : \frac{17}{12}

= \frac{17}{12}

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What is the integral from 1 to 2 of (x^2)/2+1/(2x^2) ?
The integral from 1 to 2 of (x^2)/2+1/(2x^2) is 17/12