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

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

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integral from 0 to 2 of xsqrt(1-x^2)

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

3 i + \frac{1}{3}

Solution steps

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

Apply u-substitution

: \int_{1}^{3 i} - u^{2} d u

= \int_{1}^{3 i} - u^{2} d u

Take the constant out:

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

= - \int_{1}^{3 i} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{1}^{3 i}

= - [\frac{u ^{3}}{3}]_{1}^{3 i}

Compute the boundaries:

- 3 i - \frac{1}{3}

= - (- 3 i - \frac{1}{3})

Simplify

= 3 i + \frac{1}{3}

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