Consider the integral I = ∫ 0 10 x e x e x - 1 d x where x denotes the greatest integer less than or equal to x . Then the value of I is equal to :

Question

Consider the integral I = &#8747; 0 10 x e x e x - 1 d x where x denotes the greatest integer less than or equal to x . Then the value of I is equal to :

Aicharya · Accepted Answer

I = &#8747; 0 10 x &#183; e x - x + 1 I = &#8747; 0 1 0 d x + &#8747; 1 2 1 &#183; e 2 - x + &#8747; 2 3 2 &#183; e 3 - x + &#8230; . . + &#8747; 9 10 9 &#183; e 10 - x d x &#8658; I = &#8721; n = 0 9 &#8747; n n + 1 n &#183; e n + 1 - x d x = - &#8721; n = 0 9 n e n + 1 - x n n + 1 = - &#8721; n = 0 9 n &#183; e 0 - e 1 = e - 1 &#8721; n = 0 9 n = e - 1 &#183; 9 &#183; 10 2 = 45 e - 1

Consider the integral I = ∫ 0 10 x e x e x - 1 d x where x denotes the greatest integer less than or…

Solution

Consider the integral I = &#8747; 0 10 x e x e x - 1 d x where x denotes the greatest integer less than or…

Solution

Consider the integral I = ∫ 0 10 x e x e x - 1 d x where x denotes the greatest integer less than or…