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1 year ago

Find the range of the function F(x) = the integral from 0 to x of the square root of 4-t^2 dt

1 answer:

ioda1 year ago

8 0

Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)

If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.

On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.

For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.

Then the range of F(x) is the interval [-π, π].

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B & C

Step-by-step explanation:

Use the Pythagorean Theorem: a^2 + b^2 = c^2

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2 years ago

Please Help Me! I will give all my point to who ever answers my question!!!

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Step-by-step explanation:

The equation that is given is only for the specific place of that object. To find the velocity, you need to take the derivative of the equation. This will give you:

$V=2+\frac{1}{2} t$

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Average velocity is 0.5 sec

To find instantaneous velocity just find the velocity at time one. Think about the name "instantaneous velocity," it's the velocity in that <u>instant</u>.

We already found this, so I don't need more work (it's displayed above).

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2 years ago

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Step-by-step explanation:

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2 years ago

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Step-by-step explanation:

because you would have to take the width times the height and that is 52 times 4

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