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Aim: How do we integrate Inverse Trig functions?

Aim: How do we integrate Inverse Trig functions?. Do Now:. Complete the square, express as the sum of two squares: x 2 + 4 x + 7. Differentiation Pairs & Integration. Integration will only require one formula for each pair. Integrals of Inverse Trig Functions. Model Problems. u = x 2.

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Aim: How do we integrate Inverse Trig functions?

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  1. Aim: How do we integrate Inverse Trig functions? Do Now: Complete the square, express as the sum of two squares: x2 + 4x + 7

  2. Differentiation Pairs & Integration Integration will only require one formula for each pair.

  3. Integrals of Inverse Trig Functions

  4. Model Problems u = x2

  5. Model Problems u = 3x du = 3dx u = 2x du = 2dx

  6. Model Problem – Not Quite u = ex du = exdx dx = du/ex = du/u rewrite substitute substitute/rewrite and back-substitute

  7. Model Problem Denominator is 1 term: split integrand

  8. Completing the Square sometimes: when quad functions in integrand u2 + a2

  9. Model Problem Complete the square a = 3/2 u = x - 3/2

  10. Model Problem a = 3/2; u = x - 3/2

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