What is the integral from-1 to 1 of x^2(1.5x^2) ?

The integral from-1 to 1 of x^2(1.5x^2) is 0.6

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integral from-1 to 1 of x^2(1.5x^2)

\int_{- 1}^{1} x^{2} (1.5 x^{2}) d x

0.6

Solution steps

\int_{- 1}^{1} x^{2} \cdot 1.5 x^{2} d x

Take the constant out:

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

= 1.5 \cdot \int_{- 1}^{1} x^{2} x^{2} d x

Simplify

x^{2} x^{2} : x^{4}

= 1.5 \cdot \int_{- 1}^{1} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{- 1}^{1}

= 1.5 [\frac{x ^{5}}{5}]_{- 1}^{1}

Simplify

= 1.5 [0.2 x^{5}]_{- 1}^{1}

Compute the boundaries:

0.4

= 1.5 \cdot 0.4

Simplify

= 0.6

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What is the integral from-1 to 1 of x^2(1.5x^2) ?
The integral from-1 to 1 of x^2(1.5x^2) is 0.6