What is the integral from 1 to 7 of 3x^2+1/(12x^2) ?

The integral from 1 to 7 of 3x^2+1/(12x^2) is 4789/14

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integral from 1 to 7 of 3x^2+1/(12x^2)

\int_{1}^{7} 3 x^{2} + \frac{1}{12 x ^{2}} d x

\frac{4789}{14}

Decimal

342.07142 \dots

Solution steps

\int_{1}^{7} 3 x^{2} + \frac{1}{12 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}^{7} 3 x^{2} d x + \int_{1}^{7} \frac{1}{12 x ^{2}} d x

\int_{1}^{7} 3 x^{2} d x = 342

\int_{1}^{7} \frac{1}{12 x ^{2}} d x = \frac{1}{14}

= 342 + \frac{1}{14}

Simplify

342 + \frac{1}{14} : \frac{4789}{14}

= \frac{4789}{14}

What is the integral from 1 to 7 of 3x^2+1/(12x^2) ?
The integral from 1 to 7 of 3x^2+1/(12x^2) is 4789/14