Integral of exponential: int [e^{2kx}] dx, where k is a constant

[Axl_Adler]

Hello. I just want to confirm that I'm on the right track with this question.

. . . . .\(\displaystyle \displaystyle \mbox{(b) Determine }\, \int\, e^{2kx}\, dx,\, \mbox{ where }\, k\, \mbox{ is a constant.}\)

So my initial answer was 1/2k . e^2kx + c (basically integrating exponential would stay the same, however the constants in the power of the exponential should be differentiated then divided by the equation.. i think. That was my approach, its not clear, but i hope you can understand...)

I'm just a little confused when they said k was a constant, considering c is a constant, were they referring to c or did i interpret this question correctly?

(just to add, this is probably basic, I'm just new to calculus, so its all a little confusing some times)

thank you!

 

[Deleted member 4993]

Hello. I just want to confirm that I'm on the right track with this question.

View attachment 9614

So my initial answer was 1/(2k) . e^(2kx) + c (basically integrating exponential would stay the same, however the constants in the power of the exponential should be differentiated then divided by the equation.. i think. That was my approach, its not clear, but i hope you can understand...)

I'm just a little confused when they said k was a constant, considering c is a constant, were they referring to c or did i interpret this question correctly?

(just to add, this is probably basic, I'm just new to calculus, so its all a little confusing some times)

thank you!

You solved the problem correctly - except you need to use parentheses to integrate proper hierarchy of arithmetic operations.

The statement 'k' is a constant is another way of indicating that 'x' was the only variable in the given expression (i.e. 'k' is not a variable - just like '2' is not a variable).

 

[Steven G]

Hello. I just want to confirm that I'm on the right track with this question.

View attachment 9614

So my initial answer was 1/2k . e^2kx + c (basically integrating exponential would stay the same, however the constants in the power of the exponential should be differentiated then divided by the equation.. i think. That was my approach, its not clear, but i hope you can understand...)

I'm just a little confused when they said k was a constant, considering c is a constant, were they referring to c or did i interpret this question correctly?

(just to add, this is probably basic, I'm just new to calculus, so its all a little confusing some times)

thank you!

k, in this case, is Not the constant of integration. Suppose k was 6, then the integrand would have been e^(2*3x) = e^(6*x) and the answer would have been (1/(2*3))e^(2*3x) + C = (1/6)e^(6x) + C

 

[Deleted member 4993]

k, in this case, is Not the constant of integration. Suppose k was 6, then the integrand would have been e^(2*3x) = e^(6*x) and the answer would have been (1/(2*3))e^(2*3x) + C = (1/6)e^(6x) + C

"k" → stands for Khaaaaan