Integrating ∫dx/√(4 - x²)

Calculus 2 · Axiom Academy

Evaluate this integral with the trigonometric substitution and a reference triangle. Evaluate the indefinite integral . The radical has the form with a = 2 , which is the signal for a sine substitution. Nice work — you evaluated by trigonometric substitution. Here's what carried the solution: Pattern recognition: for , the substitution collapses the radical via the Pythagorean identity. Reference triangle: drawing makes the adjacent side and the back-substitution to x immediate. Domain restriction: on we have , so with no absolute value. Don't forget dx: differentiating the substitution gives , and that is exactly what cancels. Convert back: the final answer must be in the original variable, here . The same idea handles the other two forms: uses , and uses . Identify the form first, then pick the substitution.

This is the written version of the interactive lesson above. See the full Calculus 2 course.