First integral
Since 
is a linear function, its graph is a line. This means that you can decompose the area under its graph as the sum of a right triangle and a rectangle, as shown in the attached image.
All the dimensions are fairly easy to deduce: we have
So, the area of the triangle is
For the rectangle, we have
So, the total area is 
Second integral
We have
So, this function is the upper half of the unit circle (the two halves are the functions 
)
Since the area of the unit circle is 
, the value of the integral is 
Third integral
It follows the exact same logic as the first one, you only have to adjust the numbers.
Answer:
a) maximum of 2.4 at x=-2
b) minimum of -0.3 at x=1
Step-by-step explanation:
A cubic function that is not monotonic will have one maximum and one minimum. If the leading coefficient is positive (as here), the maximum will have an x-coordinate that is less than that of the minimum.
The graph shows the extrema you're looking for.
Answer: The difference of 6 times a number m and 2
Step-by-step explanation:
The way to write this expression is:
The difference of 6 times a number m and 2.
Ms. Wilson bought 384 ounces of juice in all.
Answer:
y = 1/3 x + 2
Step-by-step explanation:
We see points (-3, 1) and (3, 3).
We also see point (0, 2), the y-intercept.
To go from (-3, 1) to (3, 3), go up 2 and right 6.
slope = m = rise/run = 2/6 = 1/3
y = mx + b
y = 1/3 x + 2
