What is the integral from 0 to 0.5 of 7arccos(x) ?

The integral from 0 to 0.5 of 7arccos(x) is 4.60301…

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integral from 0 to 0.5 of 7arccos(x)

\int_{0}^{0.5} 7 arccos (x) d x

4.60301 \dots

Solution steps

\int_{0}^{0.5} 7 arccos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int_{0}^{0.5} arccos (x) d x

Apply Integration By Parts

: [x arccos (x) - \int - \frac{x}{1 - x ^{2}} d x]_{0}^{0.5}

= 7 [x arccos (x) - \int - \frac{x}{1 - x ^{2}} d x]_{0}^{0.5}

\int - \frac{x}{1 - x ^{2}} d x = 1 - x^{2}

= 7 [x arccos (x) - 1 - x^{2}]_{0}^{0.5}

Compute the boundaries:

0.65757 \dots

= 7 \cdot 0.65757 \dots

Simplify

= 4.60301 \dots

x \to \infty lim (e^{+ x})

n = 0 \sum \infty (1 + \frac{1}{n})^{- n}

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\int \frac{( 1 + x ^{2} )}{x} d x

What is the integral from 0 to 0.5 of 7arccos(x) ?
The integral from 0 to 0.5 of 7arccos(x) is 4.60301…