Step-by-step explanation:
∫₋₂² (f(x) + 6) dx
Split the integral:
∫₋₂² f(x) dx + ∫₋₂² 6 dx
Graphically, if f(-x) = -f(x), then ∫₋₂² f(x) dx = 0. But we can also show this algebraically.
Split the first integral:
∫₋₂⁰ f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Using substitution, write the first integral in terms of -x.
∫₂⁰ f(-x) d(-x) + ∫₀² f(x) dx + ∫₋₂² 6 dx
-∫₂⁰ f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Flip the limits and multiply by -1.
∫₀² f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
Rewrite f(-x) as -f(x).
∫₀² -f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
-∫₀² f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx
The integrals cancel out:
∫₋₂² 6 dx
Evaluating:
6x |₋₂²
6 (2 − (-2))
24
I think it is (10,-7) but lmk otherwise
Answer:
Step-by-step explanation:
Here, you can use a simple formula.
To find the point of intersection you just put x=0 or y=0.
Because, if a graph intersects x-axis, then at this point y=0
Similarly, if a graph intersects y-axis, then at this point x=0
So, for our given line.
y=-1/4 x +2
when , x=0 , y=-1/4 (0)+2=2
So, the graph intersects y-axis at y=2
when , y=0 ,
then 0=-1/4 x+2
or, 1/4 x=2
or, x=8 [multiplying by 4]
So, the graph intersects x-axis at x=8
Represent the number of days by x. With this representation, the variable cost of the rental is 31.67x. The total cost is the sum of the fixed and variable costs. This value should not be more than $500. The equation below shows the relationship.
130 + 31.67x ≤ 500
Solving for x gives x ≤ 11.68
Thus, the maximum number of days to rent the car is only 11 days.
