Solve any maths problem

Equations, derivatives, integrals, matrices, triangles, primes, statistics, or a word problem the tutor breaks into parts.

Calculus · Definite-Integrals

Integrate r from 0 to 1

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

Step by step

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

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

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

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

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

    Fundamental theorem of calculus: plug in the limits.

  4. = \frac{1}{2}

    Simplify.

Reveal the answer
\frac{1}{2}