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

The integral from-1 to x of 1.5x^2 is 1.5(0.33333…x^3+0.33333…)

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integral from-1 to x of 1.5x^2

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

1.5 (0.33333 \dots x^{3} + 0.33333 \dots)

Solution steps

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

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- 1}^{x}

= 1.5 [\frac{x ^{3}}{3}]_{- 1}^{x}

Simplify

= 1.5 [0.33333 \dots x^{3}]_{- 1}^{x}

Compute the boundaries:

0.33333 \dots x^{3} + 0.33333 \dots

= 1.5 (0.33333 \dots x^{3} + 0.33333 \dots)

f (x) = \frac{x ^{5} + 4 x}{x ^{3}}

y^{^{'}} = (1 - y) \cdot sin (x)

\int_{2}^{3} \frac{18}{3 - x} d x

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

y^{^{''''}} + 2 y^{^{''}} + y = 0

What is the integral from-1 to x of 1.5x^2 ?
The integral from-1 to x of 1.5x^2 is 1.5(0.33333…x^3+0.33333…)