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

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

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

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

\frac{1}{2} arcsin (\frac{2}{3})

Decimal

0.67551 \dots

Solution steps

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

Apply Trigonometric Substitution

: \int_{0}^{a r c s i n (\frac{2}{3})} \frac{1}{2} d u

= \int_{0}^{a r c s i n (\frac{2}{3})} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{a r c s i n (\frac{2}{3})} 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2} [1 \cdot u]_{0}^{a r c s i n (\frac{2}{3})}

Simplify

= \frac{1}{2} [u]_{0}^{a r c s i n (\frac{2}{3})}

Compute the boundaries:

arcsin (\frac{2}{3})

= \frac{1}{2} arcsin (\frac{2}{3})

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