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Calculus · Definite-Integrals

Integrate 1/(x^2 + 1) from 0 to 1

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

चरणानुक्रमे

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

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

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

    Recognise an inverse-trig / inverse-hyperbolic form.

  3. F(1) - F(0) = \left(\frac{\pi}{4}\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \frac{\pi}{4} \approx 0.78540

    Simplify.

उत्तर उघडा
\frac{\pi}{4}