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 = ∫_{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= ∫_{1}^{9} (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 -
**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).

## Answer this Question

## Related Questions

- calculus (please with steps and explanations) - consider the function f that is ...
- Calculus (urgent help) - consider the function f that is continuous on the ...
- calculus - consider the function f that is continuous on the interval [-5,5] and...
- double integral - 1. Sketch the region of integration & reverse the order of ...
- Math - Use FTC to evaluate a definite integral with basic integrand-- (integral...
- calculus, help! - Evaluate the definite integral: int_{1}^{e^9} \frac{dx}{x \...
- calculus - Evaluate the definite integral: upper number of the integral is 6 ...
- Calculus Fundamental Theorem - Evaluate the definite integral. function: (t+8)(t...
- Calculus - This is a definite integral question. Evaluate the following integral...
- ap calculus - Which of the following definite integrals gives the length of y = ...