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

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

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integral from 0.5 to 1 of 1.5x^2

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

0.4375

Solution steps

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

Apply the Power Rule

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

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

Simplify

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

Compute the boundaries:

0.29166 \dots

= 1.5 \cdot 0.29166 \dots

Simplify

= 0.4375

\int (7 x + 4 y) d y

\frac{d}{d x} (\frac{( x ^{4} + 1 )}{x ^{2} - 1})

\frac{3}{x}, 12 x, \frac{1}{12} x

\frac{d}{d x} (x^{3} (1 - x)^{100} + x^{4} - 5 π)

y^{^{'}} + 7 y = 0

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