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
Answer:
Part A) The diameter of the rug is 
Part B) The radius of the rug is 
Part C) The area of the rug is 
Step-by-step explanation:
Part A) Find the diameter of the rug
we know that
The circumference of a circle (circular rug) is equal to
where
D is the diameter
we have
substitute the values and solve for D
Part B) Find the radius of the rug
we know that
The radius of a circle (circular rug) is half the diameter
we have
substitute
part C) What is the area the rug is covering?
The area of the circle (circular rug) is equal to
we have
substitute
Answer:
21 rootunder 15
Step-by-step explanation:
I think it'd be better if you gave us some sort of diagram with it?
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▹ Answer
<em>y = 15, -15</em>
▹ Step-by-Step Explanation
This is considered a 'square root' since we have to find y^2.
15 * 15 = 225
-15 * -15 = 225
Both of these values work for y, so the answer is 15, -15.
Hope this helps!
CloutAnswers ❁
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