- #1

- 40

- 0

also plz give me an example that use the definite integral to compute accumulated changes.

Thanks alot

- Thread starter gigi9
- Start date

- #1

- 40

- 0

also plz give me an example that use the definite integral to compute accumulated changes.

Thanks alot

- #2

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

e

differentiate both sides WRT x

e

x (ln x)' = 1

(ln x)' = 1 / x

so the derivative of ln x is 1/x

A relation is (to slightly modify the definition to make it easier to understand) simply a mapping from pairs of numbers to "true" or "false".

For instance:

x < y

is a relation.

Also, for any function f:

f(x) = y

is a relation. In fact,

f(x) = y and f(x) = z

can both be true only if y = z.

An example of a relation where one might use implicit differentiation is to find the slope of a point on the unit circle.

x

is a relation. Notice that y cannot be written as a

2 x + 2 y (dy/dx) = 0

2 y (dy/dx) = - 2x

(dy/dx) = -x / y

So, the slope of the tangent line to any point (x, y) of the unit circle is (dy/dx) = -x / y

Suppose I throw a ball into the air straight up with a speed of 19.6 meters per second. How high is it after 2 seconds?Thanks

also plz give me an example that use the definite integral to compute accumulated changes.

Well, acceleration is simply the rate change of velocity, so we can find the velocity at any time t with a definite integral:

v(t) - v(0) = &int

v(t) - 19.6 = &int

v(t) = 19.6 + (-9.8) * (t - 0)

v(t) = 19.6 - 9.8 t

Now, velocity is simply the rate chance of position, so we can find the height at time 2 with a definite integral:

x(2) - x(0) = &int

x(2) - 0 = &int

x(2) = [19.6 s - 4.9 s

x(2) = (19.6 * 2 - 4.9 * 2

x(2) = 19.6

So after 2 seconds, the ball is 19.6 meters high.

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 615

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 664

- Replies
- 6

- Views
- 770

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 24K

- Last Post

- Replies
- 7

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 5K