Solve any maths problem

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

Calculus · Definite-Integrals

Integrate 1/sqrt(1 - t) from 0 to 1

\int_{0}^{1} \frac{1}{\sqrt{1 - t}}\, dt

Step by step

  1. \int_{0}^{1} \frac{1}{\sqrt{1 - t}}\, dt

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

  2. u = \sqrt{1 - t},\quad du = - \frac{1}{2 \sqrt{1 - t}}\, dt

    Substitute u = \sqrt{1 - t}.

  3. \int \frac{1}{\sqrt{1 - t}}\, dt = \int -2\, d_u

    Rewrite the integral in terms of u.

  4. \int -2\, d_u = - 2 u

    The integral of a constant c is c·x.

  5. = - 2 \sqrt{1 - t}

    Substitute back u = \sqrt{1 - t}.

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

    Fundamental theorem of calculus: plug in the limits.

  7. = 2

    Simplify.

Reveal the answer
2