Question

Obtain the backward difference for the function f(x) =x^3 from x=1 to 1.05​

Answer 1

We have to find integration of f(x) having upper limit 1.05 and lower limit 1

`\\ \rm\longmapsto \displaystyle{\int^(1.05)_1}x^3dx`

`\\ \rm\longmapsto \left[(3x^(3+1))/(3+1)\right]^(1.05)_1`

`\\ \rm\longmapsto \left[(3x^4)/(4)\right]^(1.05)_1`

`\\ \rm\longmapsto (3(1.05)^4-3(1)^4)/(4)`

`\\ \rm\longmapsto (3(1.2)-3(1))/(4)`

`\\ \rm\longmapsto (3.6-3)/(4)`

`\\ \rm\longmapsto (0.6)/(4)`

`\\ \rm\longmapsto 2.4`