What is the integral from-1 to 1 of (6-6x^2)^2 ?

The integral from-1 to 1 of (6-6x^2)^2 is 192/5

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integral from-1 to 1 of (6-6x^2)^2

\int_{- 1}^{1} (6 - 6 x^{2})^{2} d x

\frac{192}{5}

Decimal Notation

38.4

Solution steps

\int_{- 1}^{1} (6 - 6 x^{2})^{2} d x

Expand

(6 - 6 x^{2})^{2} : 36 - 72 x^{2} + 36 x^{4}

= \int_{- 1}^{1} 36 - 72 x^{2} + 36 x^{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_{- 1}^{1} 36 d x - \int_{- 1}^{1} 72 x^{2} d x + \int_{- 1}^{1} 36 x^{4} d x

\int_{- 1}^{1} 36 d x = 72

\int_{- 1}^{1} 72 x^{2} d x = 48

\int_{- 1}^{1} 36 x^{4} d x = \frac{72}{5}

= 72 - 48 + \frac{72}{5}

Simplify

72 - 48 + \frac{72}{5} : \frac{192}{5}

= \frac{192}{5}

x \to \infty lim (arctan (5) - arctan (x + 1))

8 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

\frac{d y}{d x} + y^{3} x + 2 y = 0

\int \frac{2}{x} + \frac{x}{2} d x

x \to \frac{π}{2} lim (\frac{csc ( 4 x )}{csc ( 2 x )})

What is the integral from-1 to 1 of (6-6x^2)^2 ?
The integral from-1 to 1 of (6-6x^2)^2 is 192/5