What is the integral from 1 to 1000 of (25)/(x^3) ?

The integral from 1 to 1000 of (25)/(x^3) is 999999/80000

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integral from 1 to 1000 of (25)/(x^3)

\int_{1}^{1000} \frac{25}{x ^{3}} d x

\frac{999999}{80000}

Decimal Notation

12.4999875

Solution steps

\int_{1}^{1000} \frac{25}{x ^{3}} d x

Take the constant out:

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

= 25 \cdot \int_{1}^{1000} \frac{1}{x ^{3}} d x

Apply the Power Rule

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

= 25 [- \frac{1}{2 x ^{2}}]_{1}^{1000}

Compute the boundaries:

\frac{999999}{2000000}

= 25 \cdot \frac{999999}{2000000}

Simplify

= \frac{999999}{80000}

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

\frac{( x ^{2} )}{x + 2}

x \to 0 lim (\frac{cos ( \frac{π}{2} - x )}{x})

n = 2 \sum \infty 5 \cdot (- \frac{3}{4})^{n}

y^{^{''}} + 5 y^{^{'}} + 4 y = t^{2} e^{7 t}

What is the integral from 1 to 1000 of (25)/(x^3) ?
The integral from 1 to 1000 of (25)/(x^3) is 999999/80000