What is the integral from 0 to 2 of-x^2 ?

The integral from 0 to 2 of-x^2 is -8/3

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integral from 0 to 2 of-x^2

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

- \frac{8}{3}

Decimal Notation

- 2.66666 \dots

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{2}

= - [\frac{x ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= - \frac{8}{3}

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\int_{0}^{\frac{π}{2}} 4 sin (\frac{x}{2}) d x

\int_{0}^{2 π} 4 cos^{2} (x) d x

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What is the integral from 0 to 2 of-x^2 ?
The integral from 0 to 2 of-x^2 is -8/3