Page 30 - Calc for the Clueless

Rule 3

If y' = kz', then y = kz + C.

Rule 4

If y' = f' + g', then y = f + g + G.

Example 20—

Example 21—

Example 22—

2
If y' = 3x + 4x and y = 2 when x = 3, findy y.

Now x = 3, y = 2 to find G.

Rule 5

n
If y' = u du/dx with , then .
Note

Put u = x in rule 5 and you will have rule 2. We will discover that when N = -1, the antiderivative is a
logarithm.

Example 23—

99
Find y if y' = x(x + 1) .
2
We could multiply this out. On the grounds of sanity, we reject this technique.

Let u = (x + 1). du/dx = 2x.
2