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Calculus · Definite-Integrals

Integrate y^(-2) from 1 to oo

\int_{1}^{\infty} \frac{1}{y^{2}}\, dy

Step by step

  1. \int_{1}^{\infty} \frac{1}{y^{2}}\, dy

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

  2. \int \frac{1}{y^{2}}\, dy = - \frac{1}{y}

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

  3. F(\infty) - F(1) = \left(0\right) - \left(-1\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = 1

    Simplify.

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