The value of ∫ - 1 1 x 2 e x 3 d x , where t denotes the greatest integer ≤ t , is :

Question

The value of &#8747; - 1 1 x 2 e x 3 d x , where t denotes the greatest integer &#8804; t , is :

Aicharya · Accepted Answer

I = &#8747; - 1 1 x 2 e x 3 d x = &#8747; - 1 0 x 2 e x 3 d x + &#8747; 0 1 x 2 e x 3 d x = &#8747; - 1 0 x 2 e - 1 d x + &#8747; 0 1 x 2 e 0 d x = 1 e &#215; x 3 3 0 - 1 + x 3 3 0 1 = 1 e &#215; 0 - - 1 3 + 1 3 = 1 3 e + 1 3 = 1 + e 3 e

The value of &#8747; - 1 1 x 2 e x 3 d x , where t denotes the greatest integer &#8804; t , is :

Solution

The value of ∫ - 1 1 x 2 e x 3 d x , where t denotes the greatest integer ≤ t , is :