Posted by **Z32** on Tuesday, June 23, 2009 at 10:36pm.

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 -
**MathMate**, Wednesday, June 24, 2009 at 1:10am
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«_{1}^{9} (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«_{1}^{9} (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 -
**Z32**, Wednesday, June 24, 2009 at 2:53am
Thanks for the help!

- Calculus -
**MathMate**, Wednesday, June 24, 2009 at 8:38am
In case it confused you, the substituted lower limit should have read sqrt(1).

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