What is the integral from-0.5 to 0 of 1.5x^2 ?

The integral from-0.5 to 0 of 1.5x^2 is 0.0625

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integral from-0.5 to 0 of 1.5x^2

\int_{- 0.5}^{0} 1.5 x^{2} d x

0.0625

Solution steps

\int_{- 0.5}^{0} 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_{- 0.5}^{0} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- 0.5}^{0}

= 1.5 [\frac{x ^{3}}{3}]_{- 0.5}^{0}

Simplify

= 1.5 [0.33333 \dots x^{3}]_{- 0.5}^{0}

Compute the boundaries:

0.04166 \dots

= 1.5 \cdot 0.04166 \dots

Simplify

= 0.0625

x^{2} y^{^{''}} - 6 x y^{^{'}} + 10 y = 0

4 x^{3} - 4 x

\frac{d}{d x} (x^{2} - 8 ln (x))

\int e^{x} d x

x \to 0 - lim (\frac{x ^{2}}{x})

What is the integral from-0.5 to 0 of 1.5x^2 ?
The integral from-0.5 to 0 of 1.5x^2 is 0.0625