Calculus

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Evaluate the definite integral

The S thingy has 1 at the bottom and 9 at the top. 4x^2+5 divided by the sqrt of x.

  • Calculus -

    The S thingy is called the integral sign.
    The number at the bottom (1) is the lower limit of a definite integral, and the top number (9) is the upper limit of integration.

    The expression to be evaluated probably looks similar to this:

    I = ∫19 (4*x^2+5)/sqrt(x) dx

    If you use the substitution
    u=sqrt(x), then
    du=(1/2)*dx/sqrt(x)

    Substituting the limits and the variables involving x, we get
    I= ∫19 (4*x^2+5)/sqrt(x) dx

    = ∫sqrt(x)sqrt(9) (4u^4+5)*2 du
    = ∫sqrt(x)sqrt(9) (4u^4+5)*2 du

    Continuing the integration and evaluate the integral according to the integration limits, we should obtain 2036/5 as the numerical answer.

    Post if you need more details.

  • Calculus -

    Thanks for the help!

  • Calculus -

    In case it confused you, the substituted lower limit should have read sqrt(1).

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