What is the integral from 0 to 0.5 of 12x-1/12 x ?

The integral from 0 to 0.5 of 12x-1/12 x is 1.48958…

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integral from 0 to 0.5 of 12x-1/12 x

\int_{0}^{0.5} 12 x - \frac{1}{12} x d x

1.48958 \dots

Solution steps

\int_{0}^{0.5} 12 x - \frac{1}{12} x 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_{0}^{0.5} 12 x d x - \int_{0}^{0.5} \frac{1}{12} x d x

\int_{0}^{0.5} 12 x d x = 1.5

\int_{0}^{0.5} \frac{1}{12} x d x = 0.01041 \dots

= 1.5 - 0.01041 \dots

Simplify

= 1.48958 \dots

What is the integral from 0 to 0.5 of 12x-1/12 x ?
The integral from 0 to 0.5 of 12x-1/12 x is 1.48958…