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Integrals · Special Integrals

Integral yielding arcsin

∫1a2−x2 dx=arcsin⁡(xa)+C\int \frac{1}{\sqrt{a^2 - x^2}} \, dx = \arcsin\left(\frac{x}{a}\right) + C

An integral that produces the inverse sine function. Recognizing this pattern is key.

Conditions. |x| < a, a > 0.
  • 0 variables
  • 2 worked examples
  • 19 in Integrals

Worked examples

Find ∫ 1/√(9-x²) dx.
  1. a = 3. arcsin(x/3) + C

Answer: arcsin(x/3) + C

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Evaluate ∫₀^(1/2) 1/√(1-x²) dx.

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