# Thread: Finding the region under a curve

1. ## Finding the region under a curve

I have two questions here.

1. Find area of region that lies under curve y=(3x+4)1/2 over 0<x<4
(Those are less than or equal to signs)

2. It is estimated that t days from now a farmers crop will be increasing at the rate of .3t2+.6t+1 bushels per day. By how much will the value of the crop increase during the next 5 days if the market price remains fixed at \$3 a bushel?

If you can do step by step, I really don't understand this.

2. ## Re: Finding the region under a curve

Surely you know that the area under a curve f(x) between two points a and b can be calculated using $\displaystyle \int_a^b{f(x)\,dx} = F(b) - F(a)$, where F(x) is an antiderivative of f(x)...

3. ## Re: Finding the region under a curve

I have trouble finding the antiderivatives.

4. ## Re: Finding the region under a curve

For first one make substitution 3x + 4 = u that gives dx = du/3 and the limits will be from 4 to 16
the question reduces to 1/3 Integral from 4 to 16 ( u^1/2 0 du.
Now you cal finish it.