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B.B.
Lv 5
B.B. asked in Science & MathematicsMathematics · 1 decade ago

Integration troubles?

∫ √(1-x²) dx

I know that you're supposed to set x = sin(u), but why would you do that?

1 Answer

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  • 1 decade ago
    Favorite Answer

    that is the effective technique to solve the integral

    x = sinu

    dx = cosu du

    integral becomes

    ∫ cos^2u du

    = 1/2 ∫ (1 + cos(2u)) du

    = 1/2 u + 1/4 sin(2u) + C

    = 1/2 arcsin(x) + 1/2 x √(1-x²) + C

    whenever there is a quadratic with radicals involved, trigonometric substitution is the effective approach

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