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Calculus · Definite-Integrals

Integrate 1/sqrt(r) from 0 to 1

\int_{0}^{1} \frac{1}{\sqrt{r}}\, dr

Step by step

  1. \int_{0}^{1} \frac{1}{\sqrt{r}}\, dr

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

  2. \int \frac{1}{\sqrt{r}}\, dr = 2 \sqrt{r}

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

  3. F(1) - F(0) = \left(2\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = 2

    Simplify.

Reveal the answer
2