If [x] is the greatest integer function not greater than x , then ₀¹¹[x] d x is equal to

Step-by-step solution

₀¹¹[x] d x= ₀¹[x] d x+ ₁²[x] d x + ₂³[x] d x+ ₃⁴[x] d x+ ₄⁵[x] d x + ₅⁶[x] d x+ ₆⁷[x] d x+ ₇⁸[x] d x + ₈⁹[x] d x++ ₉¹⁰[x] d x++ ₁₀¹¹[x] d x= ₀ 0 d x+ ₁² 1 d x+ ₂³ 2 d x+ ₃⁴ 3 d x + ₄⁵ 4 d x+ ₅⁶ 5 d x+ ₆⁷ 6 d x+ ₇⁸ 7 d x + ₈⁹ 8 d x+ ₉¹⁰ 9 d x+ ₁₀¹¹ 10 d x=(2-1)+2(3-2)+3(4-3)+4(5-4) +5(6-5)+6(7-6)+7(8-7)+8(9-8)+9(10-9)+10(11-10)=1+2+3+4+5+6+7+8+9+10=55