Evaluate the definite integral

Question

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

Answer 1

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.

Answer 2

Thanks for the help!

Answer 3

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