What is the integral from-1 to-0.5 of 1.5x^2 ?

The integral from-1 to-0.5 of 1.5x^2 is 0.4375

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integral from-1 to-0.5 of 1.5x^2

\int_{- 1}^{- 0.5} 1.5 x^{2} d x

0.4375

Solution steps

\int_{- 1}^{- 0.5} 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}^{- 0.5} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- 1}^{- 0.5}

= 1.5 [\frac{x ^{3}}{3}]_{- 1}^{- 0.5}

Simplify

= 1.5 [0.33333 \dots x^{3}]_{- 1}^{- 0.5}

Compute the boundaries:

0.29166 \dots

= 1.5 \cdot 0.29166 \dots

Simplify

= 0.4375

(1 - x^{2}) y^{^{''}} - x y^{^{'}} + y = 0

x \to 0 lim (\frac{x ^{2} - 4}{x})

x^{4} - 4 x^{2}, x^{2} - 4

y = ln (x^{2} x + 1)

x \to 8 - lim (\frac{1}{x - 8})

What is the integral from-1 to-0.5 of 1.5x^2 ?
The integral from-1 to-0.5 of 1.5x^2 is 0.4375