(1)/(x+s)int_(-s)^(x)f(t)=(1)/(2)

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Understand the problem: Understand the problem. We are given an equation involving an integral from -5 to x of a function f(t), which is then divided by (x+5). We need to find the value of x that makes this expression equal to 1/2.Set up the equation: Set up the equation. Let's denote the integral of f(t) from -5 to x as F(x). Then the equation can be written as: (1)/(x+5) * F(x) = (1)/(2)Isolate F(x): Isolate F(x). To find F(x), we multiply both sides of the equation by (x+5): F(x) = (1)/(2) * (x+5)Evaluate F(x at the limits of integration: Evaluate F(x) at the limits of integration. Since we do not know the function f(t), we cannot directly evaluate the integral. However, we know that the integral of any function f(t) from a to a is 0, because the upper and lower limits are the same. Therefore, if x = -5, then F(-5) = 0.Check initial condition: Check if the initial condition satisfies the equation. Let's check if x = -5 satisfies the equation: F(-5) = (1)/(2) * (-5+5) F(-5) = (1)/(2) * 0 F(-5) = 0 This is consistent with our understanding that the integral from -5 to -5 of any function is 0. However, we are looking for a value of x such that the integral divided by (x+5) equals 1/2, not the integral itself.Solve for x: Solve for x. We have the equation F(x) = (1)/(2) * (x+5). Since F(x) is the integral from -5 to x of f(t), and we know that F(-5) = 0, we need to find an x such that the integral from -5 to x of f(t) divided by (x+5) equals 1/2. However, without the explicit form of f(t), we cannot proceed further to find the exact value of x. We need more information about the function f(t) to solve for x.

$\frac{1}{x+s} \int_{-s}^{x} f(t)=\frac{1}{2}$

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1x+s∫−sxf(t)=12 \frac{1}{x+s} \int_{-s}^{x} f(t)=\frac{1}{2} x+s1​∫−sx​f(t)=21​

$\frac{1}{x+s} \int_{-s}^{x} f(t)=\frac{1}{2}$