What is the integral from 1 to 1000 of (21)/(x^3) ?

The integral from 1 to 1000 of (21)/(x^3) is 20999979/2000000

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integral from 1 to 1000 of (21)/(x^3)

\int_{1}^{1000} \frac{21}{x ^{3}} d x

\frac{20999979}{2000000}

Decimal Notation

10.4999895

Solution steps

\int_{1}^{1000} \frac{21}{x ^{3}} d x

Take the constant out:

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

= 21 \cdot \int_{1}^{1000} \frac{1}{x ^{3}} d x

Apply the Power Rule

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

= 21 [- \frac{1}{2 x ^{2}}]_{1}^{1000}

Compute the boundaries:

\frac{999999}{2000000}

= 21 \cdot \frac{999999}{2000000}

Simplify

= \frac{20999979}{2000000}

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{t} cos (2 t)

(sin (6 t) - 7)^{2}

\int \frac{cos ^{2} ( θ )}{sin ( θ )} d θ

f (x) = 2^{90}

x \to 5 + lim (x^{3} - c x)

What is the integral from 1 to 1000 of (21)/(x^3) ?
The integral from 1 to 1000 of (21)/(x^3) is 20999979/2000000