What is the integral from 0 to 1 of 1/(sqrt(3-x^2)) ?

The integral from 0 to 1 of 1/(sqrt(3-x^2)) is arcsin(1/(sqrt(3)))

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integral from 0 to 1 of 1/(sqrt(3-x^2))

\int_{0}^{1} \frac{1}{3 - x ^{2}} d x

arcsin (\frac{1}{3})

Decimal Notation

0.61547 \dots

Solution steps

\int_{0}^{1} \frac{1}{3 - x ^{2}} d x

Apply Trigonometric Substitution

: \int_{0}^{a r c s i n (\frac{1}{3})} 1 d u

= \int_{0}^{a r c s i n (\frac{1}{3})} 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}{3})}

Simplify

[1 \cdot u]_{0}^{a r c s i n (\frac{1}{3})} : [u]_{0}^{a r c s i n (\frac{1}{3})}

= [u]_{0}^{a r c s i n (\frac{1}{3})}

Compute the boundaries:

arcsin (\frac{1}{3})

= arcsin (\frac{1}{3})

\int \frac{x ^{6}}{( 4 - x ^{7} ) ^{2}} d x

\frac{d}{d x} (7 sec (x) tan (x))

\int_{2}^{4} e^{3 x - y} d y

\frac{d}{d x} ((3^{\frac{2}{3}} - x^{\frac{2}{3}})^{\frac{3}{2}})

x \to 0 lim (\frac{5 x ^{2}}{2})

What is the integral from 0 to 1 of 1/(sqrt(3-x^2)) ?
The integral from 0 to 1 of 1/(sqrt(3-x^2)) is arcsin(1/(sqrt(3)))