# Please help me with this calc question?

##### 3 Answers

Have deleted answer due to an error.

#### Explanation:

The first integral

The second integral

Note that the two integrals have same value

note that

The two integrals are identical.

#### Explanation:

We seek the greater of:

# I_1 = int_a^(2a) \ 1/x \ dx # or# I_2 = int_(3a)^(6a) \ 1/x \ dx #

Where

# I(alpha,beta) = int_(alpha)^(beta) \ 1/x \ dx #

Where

# I(alpha,beta) = [ \ ln |x| \ ]_(alpha)^(beta) #

And as

# I(alpha,beta) = ln beta - ln alpha = ln (beta/alpha) #

This integral is in fact used to define the Napier logarithm and the unexpected ratio is an alternative proof of the logarithm of a product property! Given this result we now conclude that

# I_1 = ln((2a)/a) = ln 2 #

# I_2 = ln ((6a)/(3a)) =ln 2 #

Making the two integrals identical