∫ 0 5 cos π x - x 2 d x , where t denotes greatest integer less than or equal to t , is equal to

Question

&#8747; 0 5 cos &#960; x - x 2 d x , where t denotes greatest integer less than or equal to t , is equal to

Aicharya · Accepted Answer

I = &#8747; 0 5 cos x 2 &#960; - &#960; x d x &#8757; x &#8712; 0 , 5 &#160; &#8756; x &#8712; 0 , 5 2 &#8658; x 2 &#8712; 0 , 1 , 2 I = &#8747; 0 2 cos - &#960; x d x + &#8747; 2 4 cos &#960; - &#960; x d x + &#8747; 4 5 cos 2 &#960; - &#960; x d x &#8658; I = sin&#960; x &#960; 0 2 + - sin&#960; x &#960; 2 4 + sin&#960; x &#960; 4 5 = 0

&#8747; 0 5 cos &#960; x - x 2 d x , where t denotes greatest integer less than or equal to t , is equal to

Solution

∫ 0 5 cos π x - x 2 d x , where t denotes greatest integer less than or equal to t , is equal to