Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.3 Trigonometric Substitutions, #21 · Calculus · Techniques of integration

(b) How can the same integral give two answers

(Important) This section started with $x = sin θ$ and
$\int d x / 1 - x^{2} = \int d θ = θ = sin^{- 1} x$ .

(a) Use $x = cos θ$ to get a different answer.

(b) How can the same integral give two answers?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.3 Trigonometric Substitutions, #21

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