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Calculus · Definite-Integrals

Integrate sqrt(4x^2 + 1) from 0 to 1

\int_{0}^{1} \sqrt{4 x^{2} + 1}\, dx

Isigaba

  1. \int_{0}^{1} \sqrt{4 x^{2} + 1}\, dx

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

  2. \int \sqrt{4 x^{2} + 1}\, dx = \frac{x \sqrt{4 x^{2} + 1}}{2} + \frac{\operatorname{asinh}{\left(2 x \right)}}{4}

    SqrtQuadratic rule.

  3. F(1) - F(0) = \left(\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2}\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2} \approx 1.4789

    Simplify.

Bonisa impendulo
\frac{\operatorname{asinh}{\left(2 \right)}}{4} + \frac{\sqrt{5}}{2}