What is the integral from 1 to 1000 of (37)/(x^3) ?

The integral from 1 to 1000 of (37)/(x^3) is 36999963/2000000

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integral from 1 to 1000 of (37)/(x^3)

\int_{1}^{1000} \frac{37}{x ^{3}} d x

\frac{36999963}{2000000}

Decimal Notation

18.4999815

Solution steps

\int_{1}^{1000} \frac{37}{x ^{3}} d x

Take the constant out:

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

= 37 \cdot \int_{1}^{1000} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{1}^{1000}

= 37 [- \frac{1}{2 x ^{2}}]_{1}^{1000}

Compute the boundaries:

\frac{999999}{2000000}

= 37 \cdot \frac{999999}{2000000}

Simplify

= \frac{36999963}{2000000}

(\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 7 y^{3})

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

x \to + 7 lim (\frac{x}{x + 7})

\frac{\partial}{\partial x} (\frac{x e ^{y}}{3 z ^{2} + 1})

What is the integral from 1 to 1000 of (37)/(x^3) ?
The integral from 1 to 1000 of (37)/(x^3) is 36999963/2000000