Use geometry to evaluate the integral from 0 to 10 of the function f of x, dx for f of x equals 5 for x less than or equal to 5 and equals the quantity 10 minus x for x greater than 5 .
12.5
25
37.5
Cannot be found
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Steve ur being a loser with all ur comments. Enough with the attitude.
To evaluate the given integral using geometry, we can divide the area under the curve into two parts: the rectangle and the triangle.
First, let's find the area of the rectangle. The width of the rectangle is equal to 5 (from x = 0 to x = 5), and the height is equal to 5 (since f(x) = 5 for x ≤ 5). Therefore, the area of the rectangle is 5 × 5 = 25.
Next, let's find the area of the triangle. The base of the triangle is equal to 5 (from x = 5 to x = 10), and the height is equal to the difference between the maximum value of f(x) and the value at x = 10. At x = 10, f(x) = 10 - 10 = 0. So the height of the triangle is 10 - 0 = 10. Therefore, the area of the triangle is (1/2) × 5 × 10 = 25.
To find the total area under the curve, we add the area of the rectangle and the area of the triangle: 25 + 25 = 50.
However, we only need to find the integral from 0 to 10, so we divide the total area by 2: 50 / 2 = 25.
Therefore, the evaluated integral from 0 to 10 of the given function f(x) is equal to 25.
So the correct option is 25.