The area bounded by the grap of y= ex the x-a x is and line x=1&x=-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
You are correct, apologies for any confusion. Your method is correct and the solution is approximately 2.583, as you have calculated.
You know, @abdii, you really need to learn English:
say "x-axis" instead of "x-a x is"
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.
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!
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.
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.