A basic calculus question: The integral of e^2x is [(e^2x)/2] + C. Why do we only multiply by 1/2 without increasing the power?
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
you increase the power when it is x to the power of some number, when it is some number to the power or x or 2x, the rules are different.
Can you help me understand why the rule is different for e^2x than for x^2?
well, integration is (sort of) the opposite of differentiation, do you know why the derivative of x^2 is 2x?
Not the answer you are looking for? Search for more explanations.
Yes, I understand the concept.
This is an analysis question more than it is a calculus question, I suppose. Looking for what is happening under the hood conceptually to make the exp function work differently when integrating that the way other functions like the power function for instance.
e^x will stay e^x when integrated or derivative because e is a number but the power is variable
Suzi20, okay, so if I had x^2N would I not increment that exponent when integrating because it includes the variable N?
if you are integrating with respect to x, then n is not a variable, it is a constant. this is really tough to explain, maybe try khan acadmy, http://www.khanacademy.org/ they have a video that proves that the derivative of e^x is e^x.
Okay, I see the two are different and obey different rules of the road. That is what I needed to confirm. I am brand new to this and trying to get it!! THANKS. Case closed for now.