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Calculus · Definite-Integrals

Integrate 4000·pi·r^2 from 0 to 0.100000

\int_{0}^{0.1} 4000 \pi r^{2}\, dr

Step by step

  1. \int_{0}^{0.1} 4000 \pi r^{2}\, dr

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

  2. \int 4000 \pi r^{2}\, dr = 4000 \pi \int r^{2}\, dr

    Pull the constant 4000 \pi out of the integral.

  3. \int r^{2}\, dr = \frac{r^{3}}{3}

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

  4. F(0.1) - F(0) = \left(1.33333333 \pi\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  5. = 1.33333333 \pi \approx 4.1888

    Simplify.

Reveal the answer
1.33333333 \pi