The value of ∫ - π / 2 π / 2 d x x + sin ⁡ x   +   4 , where t denotes the greatest integer less than or equal to t , is

Question

The value of &#8747; - &#960; / 2 &#960; / 2 d x x + sin &#8289; x &#160; + &#160; 4 , where t denotes the greatest integer less than or equal to t , is

Aicharya · Accepted Answer

We have &#8747; - &#960; 2 &#960; 2 d x [ x ] + [ s i n x ] + 4 = &#8747; - &#960; 2 0 d x [ x ] + 3 + &#8747; 0 &#960; 2 d x [ x ] + 4 = &#8747; - &#960; 2 - 1 d x 1 + &#8747; - 1 0 d x 2 + &#8747; 0 1 d x 4 + &#8747; 1 &#960; 2 d x 5 = [ x ] - &#960; 2 - 1 + x 2 - 1 0 + x 4 0 1 + x 5 1 &#960; 2 = - 1 + &#960; 2 + 0 + 1 2 + 1 4 + &#960; 10 - 1 5 = - 20 + 10 &#960; + 10 + 5 + 2 &#960; - 4 20 = 12 &#960; - 9 20 = 3 20 4 &#960; - 3

The value of ∫ - π / 2 π / 2 d x x + sin ⁡ x   +   4 , where t denotes the…

Solution

The value of &#8747; - &#960; / 2 &#960; / 2 d x x + sin &#8289; x &#160; + &#160; 4 , where t denotes the…

Solution

The value of ∫ - π / 2 π / 2 d x x + sin ⁡ x + 4 , where t denotes the…