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

The integral from-2 to 2 of (3-(x^2-1)) is 32/3

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

\int_{- 2}^{2} (3 - (x^{2} - 1)) d x

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

\int_{- 2}^{2} 3 - (x^{2} - 1) d x

Simplify

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

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

\int_{- 2}^{2} 4 d x = 16

= - \frac{16}{3} + 16

Simplify

- \frac{16}{3} + 16 : \frac{32}{3}

= \frac{32}{3}

\int \frac{x ^{\frac{1}{3}}}{x ^{\frac{2}{3}}} d x

f (x) = 3 x^{2} - 4 x + 3

\int 8 x^{7} e^{4 x^{8}} d x

\int_{1}^{2} \frac{1}{8} (2 + 2 x - x^{2}) d x

\int \frac{x ^{2}}{( 1 + x ^{3} )} d x

What is the integral from-2 to 2 of (3-(x^2-1)) ?
The integral from-2 to 2 of (3-(x^2-1)) is 32/3