# Integration in solving work

#### lauriecherie

1. Homework Statement

can someone please explain to me how to intergrate this:

the definite integral from 0 to PI of (.25*PI) (1+kh) g (h + .2) dh

I can leave g, PI, and k in the formula.

2. Homework Equations

3. The Attempt at a Solution

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#### slider142

What have you attempted? Do you know how to integrate polynomials?

#### lauriecherie

I'm not sure what I need to do. The k is what's causing me problems. I tried factoring but that got me no where. Can you explain what I need to do or explain to me how the book got this answer to this integral? This one of course isn't my problem but can you explain how they intergrated this one? It is similiar to the one I need to solve.

The definite integral from 0 to 1.5 of (.25 * PI) (1 + kh) g (h + 0.3) dh

The answer: .366 (k + 1.077) gPI

#### CFDFEAGURU

Integrate the function with respect to h and then insert the upper value of the integral for h and then do the same for the lower value of the integral and subtract the two.

#### CFDFEAGURU

Remember that constants come outside the integral.

#### lauriecherie

Ok so I can pull out PI, g, and .25? Or just PI and g?

And do i distribute (1 + kh) * (h + .2)???

#### slider142

Is k a constant (A number which does not depend on the variable of integration h)? If so, remember this rule of integration of two integrable functions f and g:
$$\int (f + g) = \int f + \int g$$
and if k is a constant:
$$\int kf = k\int f$$
Also, remember the power rule of differentiation:
$$\frac{d}{dx}(x^n) = nx^{n-1}$$
from which we get:
$$\int x^n dx = \frac{x^{n+1}}{n+1} + C$$
where C is an arbitrary constant of integration.
The best course of action is then to multiply everything out so that you are left with a polynomial, where you can integrate each term in the sum separately.

#### lauriecherie

So I'm getting...

.25*PI*g * (The definite integral from 0 to 1.5 of (h + kh^2 + .2 + .2kh).

I don't know what to do with this k.

If I integrate I'm getting

.25*PI*g * { (h^2/2) + ((kh^3)/(3)) + (.2h) + (.1k*h^2)} evaluated from 0 to 1.5

#### Redbelly98

Staff Emeritus
Homework Helper
Looks good, now just evaluate it with the limits 0 to 1.5.

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