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Calculus · Definite-Integrals

Integrate w^(-2) from 2 to oo

\int_{2}^{\infty} \frac{1}{w^{2}}\, dw

Step by step

  1. \int_{2}^{\infty} \frac{1}{w^{2}}\, dw

    First find an antiderivative F, then evaluate F(b) − F(a).

  2. \int \frac{1}{w^{2}}\, dw = - \frac{1}{w}

    Power rule: ∫xⁿ dx = xⁿ⁺¹/(n+1) (n ≠ −1).

  3. F(\infty) - F(2) = \left(0\right) - \left(- \frac{1}{2}\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \frac{1}{2}

    Simplify.

Reveal the answer
\frac{1}{2}