In this we need to approximate definite integral by midpoint formula.
According to this formula if we have to calculate
then we will divide the interval [a,b] into n subinterval of equal width.
Δx =
So we will denote each of interval as follows
where
Then for each interval we will calculate midpoint.
So we can calculate definite integral as
where
are midpoint of each interval.
So in given question we need to calculate
. So we will divide our interval in 6 equal parts.
Given interval is [1,2]
So we will denote 6 interval as follows
Now midpoint of each interval is
So
for the given function is
So
First of all, how much juice is there?
So,
Then,
Therefore,
of juice is left in Luna's glass.
Hope this helps!!! ;)
What subject is this if this is math I am good at it
To answer the 1 and 2 just put 0 on the variable other than the intercept you are looking for, if your looking for X, then Y = 0 so...
(Option D)1. -10x+5y=40
intercept on X
-10x + 5(0)=40
-10x=40 (divide by -10 to take x alone)
x= -4
intercept on Y
-10(0)+5y=40
5y=40 (divide by 5)
y=8
(Option D) 2. same procedure
int. X
5x +4y =80
5x + 4(0) = 80
x = 16
int y.
5(0) + 4y = 80
y = 20
3. just put in standard mode
y= (1/6)x + 4 (multiply by 6 so you have dont have fractions)
6y= x+ 24 (move x to the other side)
-x + 6y = 24