`int_0^([x])(x-[x])dx=([x])/2`

Statement-1: int_0^([x]) 4^(x-[x])dx=(3[x])/(2log2) ,Statement-2: int_0^([x]) a^(x-[x])dx=[x]int_0^1 a^(x-[x])dx (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: int_0^([x]) 4^(x-[x])dx=(3[x])/(2log2) ,Statement-2: int_0^([x]) a^(x-[x])dx=[x]int_0^1 a^(x-[x])dx (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Prove that int_(0)^(x)[x]dx=x[x]-(1)/(2)[x]([x]+1)

Prove that int_(0)^(x) [x]dx=[x]([x]-1)/(2)+[x] (x-[x]) , where [.] denotes the greatest integer function

Show that: int_0^x[x]dx=[x]([x]-1)/2+[x](x-[x]) , where [x] denotes the integral part of x .

int_0^2{x}^([x])dx

Show that: (int_0^[x] [x]dx)/(int_0^[x] {x}dx)=[x]-1 , where [x] denotes the integral part of x and {x}=x-[x] .

Show that: (int_0^[x] [x]dx/(int_0^[x] {x}dx)=[x]-1 , where [x] denotes the integral part of x and {x}=x-[x] .

int_0^1 (x+x^2)dx