If ∫ - a a x + x - 2 d x = 22 ,   a > 2 and x denotes the greatest integer ≤ x , then ∫ a - a x + x d x is equal to

Question

If &#8747; - a a x + x - 2 d x = 22 , &#160; a &#62; 2 and x denotes the greatest integer &#8804; x , then &#8747; a - a x + x d x is equal to

Aicharya · Accepted Answer

&#8747; - a 0 - 2 x + 2 d x + &#8747; 0 2 x + 2 - x d x + &#8747; 2 a 2 x - 2 d x = 22 &#8658; - x 2 + 2 x | - a 0 + 2 x | 0 2 + x 2 - 2 x | 0 a = 22 &#8658; a 2 + 2 a + 4 + a 2 - 2 a = 22 &#8658; 2 a 2 = 18 &#8658; a = 3 &#160; ( a &#8800; - 3 ) &#8747; 3 - 3 x + x d x = &#8747; 3 - 3 x d x + &#8747; 3 - 3 x d x = 0 + - - 3 - 2 - 1 + 1 + 2 = 3

If ∫ - a a x + x - 2 d x = 22 ,   a > 2 and x denotes the greatest integer ≤ x , then…

Solution

If &#8747; - a a x + x - 2 d x = 22 , &#160; a &#62; 2 and x denotes the greatest integer &#8804; x , then…

Solution

If ∫ - a a x + x - 2 d x = 22 , a > 2 and x denotes the greatest integer ≤ x , then…