What is the integral from 0 to 1 of 1/(sqrt(16-x^2)) ?

The integral from 0 to 1 of 1/(sqrt(16-x^2)) is arcsin(1/4)

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integral from 0 to 1 of 1/(sqrt(16-x^2))

\int_{0}^{1} \frac{1}{16 - x ^{2}} d x

arcsin (\frac{1}{4})

Decimal

0.25268 \dots

Solution steps

\int_{0}^{1} \frac{1}{16 - x ^{2}} d x

Apply Trigonometric Substitution

= \int_{0}^{a r c s i n (\frac{1}{4})} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{0}^{a r c s i n (\frac{1}{4})}

Simplify

= [u]_{0}^{a r c s i n (\frac{1}{4})}

Compute the boundaries:

arcsin (\frac{1}{4})

= arcsin (\frac{1}{4})

What is the integral from 0 to 1 of 1/(sqrt(16-x^2)) ?
The integral from 0 to 1 of 1/(sqrt(16-x^2)) is arcsin(1/4)