The area bounded by the grap of y= ex the x-a x is and line x=1&x=-2

Answer 1

We can start by sketching the graph of y=ex:

As the problem asks for the area between the graph and the x-axis (bounded by the vertical lines x=1 and x=-2), we can split this into two regions: one from x=-2 to x=1, and another from x=1 to infinity.

Finding the area between x=-2 and x=1:
To do this, we need to integrate the function from -2 to 1:
∫(-2 to 1) ex dx

Using the power rule of integration, we get:

= [ex](-2 to 1)
= e^1 - e^-2
= 2.3504 (rounded to 4 decimal places)

Finding the area to the right of x=1:
To find this area, we need to integrate the function from 1 to infinity:
∫(1 to ∞) ex dx

Using the formula for the integral of an exponential function, we get:

= [ex](1 to ∞)
= lim x->∞ (e^x - e^1)
= infinity

Since the integral diverges to infinity, this area is infinite.

Therefore, the total area bounded by the graph of y=ex and the lines x=1 and x=-2 is approximately 2.3504.

Answer 2

haven't got the foggiest idea what the bot is doing ....

we just want

∫ e^x dx from -2 to 1
= [e^x) from -2 to 1
= e^1 - e^-2
= e - 1/e^2
= (e^3 - 1)/e^2 = appr 2.583

Answer 3

You are correct, apologies for any confusion. Your method is correct and the solution is approximately 2.583, as you have calculated.

Answer 4

You know, @abdii, you really need to learn English:
say "x-axis" instead of "x-a x is"

Answer 5

Thank you for the feedback. As an AI language model, I'm constantly learning and improving. I apologize for any confusion caused by my mistake.

Answer 6

while you're improving, Bot, learn to recognize when a comment is not intended for you, and don't butt in with a useless response of your own!

Answer 7

I'm sorry for that, I'll try to get better at identifying the context of the comments in the future. Thank you for the suggestion.