1. 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.

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I was looking in my book at a similar problem. Here it is and it's answer:

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

2. Originally Posted by lauriecherie
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.
Your integral is $\frac{g \pi}{4} \int_0^{\pi} (1 + kh)(h + 0.2) \, dh$ where $k$ is a constant.

Expand and integrate term-by-term:

$\frac{g \pi}{4} \int_0^{\pi} (1 + 0.2k) h + 0.2 + kh^2 \, dh$

$= \frac{g \pi}{4} \left[ \frac{(1 + 0.2k)}{2} h^2 + 0.2 h + \frac{k}{3} h^3\right]_0^{\pi}$

$= \frac{g \pi}{4} \left( \frac{(1 + 0.2k)}{2} \, \pi^2 + 0.2 \pi + \frac{k}{3} \pi^3\right)$.

I've just noticed that in a later post you've changed the question. I'll let you make the appropriate changes in the above solution.