Computing an integral by substitution is the reverse of the chain rule for computing the derivative. Substitution is intended to rewrite a complicated-looking integral involving the derivative of some component expression as another much simpler integral. For example, if 
, then 
and
###
Integration by parts is the reverse of the product rule for derivatives:
Integrating both sides with respect to 
gives
###
Personally, I think the best way to grasp the idea behind the two methods is to practice. You start to notice patterns to the point where knowing which is the "right" method to use becomes second nature.
Answer:
A) 46 mph
Step-by-step explanation:
<em>Step 1: To find the speed, you need to find the distance and time to travel between Chicago and Cleveland.</em>
Distance = 354 miles
Time = 9: 50 am to 5: 30 pm
Time = 7 hours 40 minutes
<em>Step 2: Convert time to hours</em>
1 hour = 60 minutes
40 minutes = 60/40 = 2/3 hours
<em>Step 3: Find the speed</em>
Speed = Distance/Time
Speed = 354/7 + 2/3
Speed = 1062/23
Speed = 46.17 miles per hour rounded off to 46 mph
Therefore, A is the correct answer.
!!
Answer:
The maximum amount of loan should be $25000
Step-by-step explanation:
we are given
In the inequality 2x + $15,000 is less then equal to $65,000
where
x represents the amount of a car loan
so, we get inequality as
Firstly, we will solve for x
We will subtract both sides by 15000
Divide both sides by 2
we get
So,
The maximum amount of loan should be $25000
First, subtract x from both sides of the equation. Second, divide by 4 on both sides of the equations. At this point you should have y= 3 - x because 12 divided by 4 equals 3. So, to get it into slope intercept form (since slope intercept form is y = mx + b) in the end you should have y = -x + 3. :)
