# 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 = âˆ«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= âˆ«19 (4*x^2+5)/sqrt(x) dx

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