How to find the definite integral of e to the power (- x) from negative infinity to 0 The specific problem is as follows: when x is greater than or equal to 0, find f (x) = (1 / 2) [∫ e ^ (- x) DX (integral lower limit is negative infinity, upper limit is 0)] + (1 / 2) [∫ e ^ (- x) DX (integral lower limit is 0, upper limit is x)]

How to find the definite integral of e to the power (- x) from negative infinity to 0 The specific problem is as follows: when x is greater than or equal to 0, find f (x) = (1 / 2) [∫ e ^ (- x) DX (integral lower limit is negative infinity, upper limit is 0)] + (1 / 2) [∫ e ^ (- x) DX (integral lower limit is 0, upper limit is x)]

The definite integral from negative infinity to zero is - 1 / 2 + 1 / 2 * e (infinite power), that is, positive infinity
From the answer, the original function should be:
F (x) = (1 / 2) [∫ e ^ (x) DX (integral lower limit is negative infinity, upper limit is 0)] + (1 / 2) [∫ e ^ (- x) DX (integral lower limit is 0, upper limit is x)]