Solving Integral of e^6x with U Substitution

In summary: You've differentiated y wrt x. It's correct, just not what you wanted to find.In summary, the conversation discusses the use of different notations for solving a calculus problem involving the integral of e^6x. The first notation uses u substitution while the second notation uses dy/dx = dy/du * du/dx. Both notations are correct, but one is for integration while the other is for differentiation. The confusion lies in the difference between these two operations.
  • #1
wiredmomar
1
0
Hey All,

First post, hopefully it will be readable. I was going to try and word it correctly, but I might as well just post a problem I am having with a certain notation.

Take integral of e^6x. Easy enough question. Using U substitution:

u = 6x
du/dx = 6
du = 6 dx

Integral above now equals 1/6 e^6x + C (so the 1/6 cancels with our 6 in 6 dx).

Ok, now using dy/dx = dy/du * du/dx notation.

e^6x let u = 6x
y = e^u
u = 6x

dy/du = e^u
du/dx = 6

Since dy/dx = dy/du * du/dx, wouldn't the above equal e^6x * 6

The second notation confuses me a bit... Any help to explain would be appreciat
Thanks,

M
 
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  • #2
dy/dx=6e^6x is correct,
if y=e^6x

You've differentiated y wrt x. It's correct, just not what you wanted to find.
 
  • #3
wiredmomar said:
Hey All,

First post, hopefully it will be readable. I was going to try and word it correctly, but I might as well just post a problem I am having with a certain notation.

Take integral of e^6x. Easy enough question. Using U substitution:

u = 6x
du/dx = 6
du = 6 dx

Integral above now equals 1/6 e^6x + C (so the 1/6 cancels with our 6 in 6 dx).

Ok, now using dy/dx = dy/du * du/dx notation.

e^6x let u = 6x
y = e^u
u = 6x

dy/du = e^u
du/dx = 6

Since dy/dx = dy/du * du/dx, wouldn't the above equal e^6x * 6
Yes, it would. One is integrating, the other differentiating. Since those are "opposite" operations, it shouldn't surprise you that one involves dividing by 6 and the other involves multiplying by 6.

The second notation confuses me a bit... Any help to explain would be appreciat
Thanks,

M
 

Related to Solving Integral of e^6x with U Substitution

1. How do I identify a problem that requires U substitution to solve the integral of e^6x?

Problems that require U substitution typically involve integrals with a function raised to a power, such as e^6x, and a variable in the exponent that can be rewritten as a function of another variable using the chain rule.

2. What is the general process for solving an integral of e^6x with U substitution?

The general process for solving an integral of e^6x with U substitution involves identifying the function that can be rewritten as a function of u, substituting u for that function, and then solving the integral using the substitution method.

3. How do I choose the appropriate u for U substitution?

The appropriate u for U substitution is usually the function inside the parentheses that can be rewritten as a function of u, but it can also be any variable or expression that will simplify the integral.

4. What do I do with the du in the U substitution process?

After choosing the appropriate u, you will need to find the corresponding du using the chain rule. The du will then be substituted into the integral along with u, and the integral will be rewritten in terms of u and du.

5. Are there any common mistakes to avoid when solving an integral of e^6x with U substitution?

One common mistake to avoid is forgetting to substitute u and du into the integral after finding them. Another mistake is not properly simplifying the integral after substitution, which can lead to incorrect solutions.

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