What is the integral of 0.75(1-x^2) ?

The integral of 0.75(1-x^2) is 0.75(x-0.33333…x^3)+C

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integral of 0.75(1-x^2)

\int 0.75 (1 - x^{2}) d x

0.75 (x - 0.33333 \dots x^{3}) + C

Solution steps

\int 0.75 (1 - x^{2}) d x

Take the constant out:

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

= 0.75 \cdot \int 1 - x^{2} 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

= 0.75 (\int 1 d x - \int x^{2} d x)

\int 1 d x = x

\int x^{2} d x = \frac{x ^{3}}{3}

= 0.75 (x - \frac{x ^{3}}{3})

Simplify

= 0.75 (x - 0.33333 \dots x^{3})

Add a constant to the solution

= 0.75 (x - 0.33333 \dots x^{3}) + C

What is the integral of 0.75(1-x^2) ?
The integral of 0.75(1-x^2) is 0.75(x-0.33333…x^3)+C