What is the integral from-3 to 3 of (15-x^2)-(x^2-3) ?

The integral from-3 to 3 of (15-x^2)-(x^2-3) is 72

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integral from-3 to 3 of (15-x^2)-(x^2-3)

\int_{- 3}^{3} (15 - x^{2}) - (x^{2} - 3) d x

72

Solution steps

\int_{- 3}^{3} 15 - x^{2} - (x^{2} - 3) d x

Simplify

= \int_{- 3}^{3} - 2 x^{2} + 18 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_{- 3}^{3} 2 x^{2} d x + \int_{- 3}^{3} 18 d x

\int_{- 3}^{3} 2 x^{2} d x = 36

\int_{- 3}^{3} 18 d x = 108

= - 36 + 108

Simplify

= 72

\int \frac{- 4}{cos ( x ) - 1} d x

6 (ln (y)) y^{^{'}} - x^{3} y = 0

x \to \frac{π}{2} lim (9 sec (x))

x \to \infty lim (\frac{1}{x} - 2)

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

What is the integral from-3 to 3 of (15-x^2)-(x^2-3) ?
The integral from-3 to 3 of (15-x^2)-(x^2-3) is 72