The positive value of x satisfying the equati | vedclass

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(D) Given the equation $\int_x^1(1-t) dt = \frac{1}{2}$.Evaluating the integral: $\left[t - \frac{t^2}{2}\right]_x^1 = \frac{1}{2}$.Substituting the l

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$2$

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(D) Given the equation $\int_x^1(1-t) dt = \frac{1}{2}$.Evaluating the integral: $\left[t - \frac{t^2}{2}\right]_x^1 = \frac{1}{2}$.Substituting the limits: $(1 - \frac{1}{2}) - (x - \frac{x^2}{2}) = \frac{1}{2}$.$\frac{1}{2} - x + \frac{x^2}{2} = \frac{1}{2}$.Subtracting $\frac{1}{2}$ from both sides: $\frac{x^2}{2} - x = 0$.Multiplying by $2$: $x^2 - 2x = 0$.Factoring: $x(x - 2) = 0$.Thus,$x = 0$ or $x = 2$.Since the question asks for the positive value of $x$,we have $x = 2$.

The positive value of $x$ satisfying the equation $\int_x^1(1-t) dt = \frac{1}{2}$ is

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