Answer:
Step-by-step explanation:
.
It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.
Integration by substitution involves swapping the variable 
for another variable which depends on x: 
. (We are going to choose 
for this question).
The very first step is to choose a suitable substitution. That is, an equation 
which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution 
.
Your integral contains the term 
. The derivative is 
and (ignoring the constants) we see is also in the integral and so the substitution 
will unravel this integral!
Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").
Then,
.
The substitution has made this integral is easy to solve!
Finally we can substitute back to get the answer in terms of x:
Answer:
40
Step-by-step explanation:
Answer:
x = {0.449489743, -4.449489743} thats what i got
Answer: f(x) = x/2 + 4.
where f(x) is the number of stamps that Tom has, and x is the number of stamps that Myrna has.
Step-by-step explanation:
The statement is:
"Tom has four more than half the stamps that Myrna has"
For how is written, we can model the number of stamps that Tom has as a function f(x).
f(x) represents the number of stamps that Tom has, and x is the number of stamps that Myrna has.
Then:
"four more than a number" is written as:
N + 4 (where N is the number)
"Half the stamps that Myrna has" is written as:
x/2.
Then the whole statement can be modeled as:
f(x) = x/2 + 4.
notice that we have x/2, and f(x) must be a whole number, so Myrna must have an even number of stamps (in that case x/2 will be integer)
