What is the integral from 0 to 0.5 of 300x ?

The integral from 0 to 0.5 of 300x is 37.5

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integral from 0 to 0.5 of 300x

\int_{0}^{0.5} 300 x d x

37.5

Solution steps

\int_{0}^{0.5} 300 x d x

Take the constant out:

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

= 300 \cdot \int_{0}^{0.5} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{0.5}

= 300 [\frac{x ^{2}}{2}]_{0}^{0.5}

Simplify

= 300 [0.5 x^{2}]_{0}^{0.5}

Compute the boundaries:

0.125

= 300 \cdot 0.125

Simplify

= 37.5

x^{2} y^{^{''}} + 7 x y^{^{'}} + 5 y = 0, y (1) = 0, y^{^{'}} (1) = 2

\frac{\partial}{\partial x} (x \cdot y^{2})

x \to 0 lim ((1 + \frac{x}{2})^{\frac{1}{x}})

- x^{2} + 8 x, x^{2} - 4 x

\frac{d}{d x} (∣ x ∣^{∣ c o s (x) ∣})

What is the integral from 0 to 0.5 of 300x ?
The integral from 0 to 0.5 of 300x is 37.5