Expert: Paul Klarreich - 9/1/2009

Question
For any t > or = to 0, let A(t) be the area of the right triangle bounded above by the line y=x, below by the x-axis, and on the right by the line x=t.

Write a formula for A(t).

i cannot figure this question out and any help would be appreciated.  

Answer
Questioner: Jeff
Country: United States
Category: Calculus
Private: No
Subject: Summer AP Calc Packet Help
Question: For any t > or = to 0, let A(t) be the area of the right triangle bounded above by the line y=x, below by the x-axis, and on the right by the line x=t.

Write a formula for A(t).

i cannot figure this question out and any help would be appreciated.
...........................................................
Hi, Jeff,

If you wish to succeed in AP Calc, you have to make up your mind that:

YOU WILL DRAW GOOD DIAGRAMS.

Such as this one isn't but it's the best I can do here:

      +  <-----  (t,t)
     /|
    / |
   /  |
| /   |
|/    |
-+-----+-
|     t

The diagonal is your  y = x, and the point at the top is (t,t). [I leave it to you to work out why.]

Then you will make up your mind that:

YOU WILL LOOK UP THE FORMULAS NEEDED AND MEMORIZE THEM.

such as:

Area of a triangle = 1/2  base * height.

Now you know how to finish up.