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

The integral from 0 to 1 of xsqrt(2-x^2)-x^3 is (2sqrt(2)-1)/3-1/4

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

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

\frac{2 2 - 1}{3} - \frac{1}{4}

Decimal

0.35947 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int_{0}^{1} x^{3} d x = \frac{1}{4}

= \frac{2 2 - 1}{3} - \frac{1}{4}

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\int_{0}^{1} θ^{2} + 1 d θ

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

What is the integral from 0 to 1 of xsqrt(2-x^2)-x^3 ?
The integral from 0 to 1 of xsqrt(2-x^2)-x^3 is (2sqrt(2)-1)/3-1/4