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

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

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

\int_{- 2}^{2} - (1 - x^{2}) d x

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

\int_{- 2}^{2} - (1 - x^{2}) d x

Take the constant out:

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

= - \int_{- 2}^{2} 1 - x^{2} 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_{- 2}^{2} 1 d x - \int_{- 2}^{2} x^{2} d x)

\int_{- 2}^{2} 1 d x = 4

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

= - (4 - \frac{16}{3})

Simplify

- (4 - \frac{16}{3}) : \frac{4}{3}

= \frac{4}{3}

\int_{5}^{7} ∣ f (3 x) ∣ d x

\int_{0}^{15} x d x

\int_{0}^{1} (x + 3) e^{2 x} d x

\int_{3}^{7} 3 d x

\int_{1}^{4} - \frac{6}{x ^{2}} d x

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