Asked by Z32

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.

Answers

Answered by MathMate
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 = ∫<sub>1</sub><sup>9</sup> (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= ∫<sub>1</sub><sup>9</sup> (4*x^2+5)/sqrt(x) dx

= ∫<sub>sqrt(x)</sub><sup>sqrt(9)</sup> (4u^4+5)*2 du
= ∫<sub>sqrt(x)</sub><sup>sqrt(9)</sup> (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.
Answered by Z32
Thanks for the help!
Answered by MathMate
In case it confused you, the substituted lower limit should have read sqrt(1).
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