1) It is known that if *m* *f*(*x*) *M* for *a* *x* *b*, then the following property of integrals is true. $\displaystyle m(b-a) <= \int^b_a f(x)dx <= M(b-a)$

Use this property to estimate the value of the given integral.

____ __<__ $\displaystyle \int^6_0 3xe^{-x}dx$ __<__ ____

Would I just have to find the minimum and maximum on that interval, then plug everything in?

2) Code:

f(x) = {
0 if x < 0
x if 0 <= x <= 1
2 - x if 1 <= x <= 2
0 if x > 2
}

$\displaystyle g(x) = \int ^x_0 f(t)dt$

(a) Find an expression for *g*(*x*) similar to the one for *f*(*x*).

Give your answer in the form below.

State where g(x) is discontinuous (if anywhere)

I've done everything but H and K, which I think I need to decide if it's continuous or not. I thought K would just be the Integral of 0, but that's not right, and I'm not sure how to go about solving for H on this one.