please could anyone explain this step ∫1/(2a)√(u) du = a²/3.?

u = (a² - x²)

2 Answers

  • 9 years ago
    Favorite Answer

    That "a" is a constant and the integral is taken from u=0 to u=a. (That is from x=a to x=0, but "x" is irrelevant.)

    By the constant and power rules for integrals:

         ∫1/(2a)√(u) du = [1/(2a)] u^(3/2) / (3/2) + C = u^(3/2) / (3a) + C

    Substituting u=a (which gives a^(3/2)/(3a)+C=a²/3+C) and u=0 (which gives 0+C=C) and subtracting produces the required result.

    Source(s): Review your integration rules!
  • D g
    Lv 7
    9 years ago

    is the square root on the denominator or numerator

    the equation in the integral is it 1/(2a * sqrt (u)) or is it


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