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].
Answer:
x=5
Step-by-step explanation:
We can use proportions to solve this problem. Put the side of the small triangle over the side of the large triangle.
9 15
------ = ----------
2x-1 3x
Using cross products
9*3x = 15(2x-1)
27x = 30x-15
Subtract 30x from each side
27x-30x = 30x-30x -15
-3x = -15
Divide by -3
-3x/-3 = -15x/-3
x = 5
Hello macelynn190!
To solve this question we need to substitute the given values of 'a' & 'b' in the equation & then simplify it.
Given,
Now, substitute this in the place of 'a' & 'b'..
Lastly, simplify it...
- The answer is <u>-</u><u>9</u><u>/</u><u>2</u><u> </u><u>or </u><u>-</u><u>4</u><u>.</u><u>5</u>
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Hope it'll help you!
ℓu¢αzz ッ
