Help with definate integration problem

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The forum discussion focuses on solving the definite integral \(\int_{1}^{2} 10^{t} dt\). The user initially struggles with the integration due to the presence of a logarithmic function in the denominator when evaluating the integral at the bounds. The correct solution is confirmed to be \(\frac{90}{\ln(10)}\), and a clarification is made regarding the substitution rule, emphasizing the correct placement of variables in the integration formula.

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Homework Statement



[tex]\int[/tex]10[tex]^{t}[/tex]dt t = [1,2]

Homework Equations



I know that [tex]\int[/tex](a[tex]^{x}[/tex])dx = [tex]\frac{(a^x)}{ln(x)}[/tex] + C and x[tex]\neq[/tex] 1

The Attempt at a Solution



I could do this problem as indefinate, but since the restraints include a "1", I can't plug it into the the integral because it will result in a "0" being in the denominator. The answer in the back of the book shows:

[tex]\frac{90}{ln(10)}[/tex]

Should I be using a substitution rule somewhere?
 
Last edited:
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Well, the equation in your section 2 is actually incorrect, the x and a's should be switched around ( or the dx replaced with da). That solves the problem !
 
sorry never mind, its supposed to be the ln(a) not x
 

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