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MathCalculus

Trig Substitution: Evaluate ∫√(4 − x²) dx

Use x = 2 sin θ to evaluate OpenStax Calculus Volume 2 exercise 136, then return the answer to x and check its domain.

Question

OpenStax Calculus Volume 2, §3.3, exercise 136: Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable.

∫4−x2 dx\int\sqrt{4-x^2}\,dx

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Evidence boundary

The source asks for an indefinite integral, with no initial condition. The additive constant remains arbitrary. The standard two-sided derivative check is on (−2,2)(-2,2).