The value of α for which 4 α ∫ - 1 2 e - α x d x = 5 , is

Question

The value of &#945; for which 4 &#945; &#8747; - 1 2 e - &#945; x d x = 5 , is

Aicharya · Accepted Answer

4 &#945; &#8747; - 1 0 e &#945; x d x + &#8747; 0 2 e - &#945; x d x = 5 &#8658; 4 &#945; e &#945; x &#945; - 1 0 + e - &#945; x - &#945; &#8203; 0 2 = 5 &#8658; 4 &#945; 1 - e - &#945; &#945; - e - 2 &#945; - 1 &#945; = 5 &#8658; 4 2 - e - &#945; - e - 2 &#945; = 5 Put e - &#945; = t &#8658; 4 t 2 + 4 t - 3 = 0 &#8658; 2 t + 3 2 t - 1 = 0 &#8658; e - &#945; = 1 2 &#8658; &#945; = ln 2

The value of &#945; for which 4 &#945; &#8747; - 1 2 e - &#945; x d x = 5 , is

Solution

The value of α for which 4 α ∫ - 1 2 e - α x d x = 5 , is