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March 29, 2017

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integral[7 sqrt 2/2,0]sqrt(49+x^2) dx

  • Calculus - ,

    x = 7 sinh(t)

    sqrt(49 + x^2) = 7 sqrt[1 + sinh^2(t)] = 7 cosh(t)

    dx = 7 cosh(t) dt

    The integral is thus:

    49 Integral of cosh^2(t) dt =

    49 Integral of [cosh(2t) + 1]/2 dt =

    49 [t/2 + 1/4 sinh(2t)]

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