Question

If ƒ(x) is continuous for all real values of x, then (r – 1 + x) dx is equal to –

• A. dx
• B. dx
• C. ndx
• D. (n – 1) dx

Answer 1

Answer: (A)

dx

Answer 2

(r – 1 + x) dx

= $\int _ { 0 } ^ { 1 } f$ (x) dx + $\int _ { 0 } ^ { 1 } f$ (1 + x) dx + $\int _ { 0 } ^ { 1 } f$ (2 + x) dx

+ …. + $\int _ { 0 } ^ { 1 } f$ (n – 1 + x) dx

= $\int _ { 0 } ^ { 1 } f$ (x) dx + $\int _ { 1 } ^ { 2 } f$ (x) dx + $\int _ { 2 } ^ { 3 } f$ (x) dx + …. + (x) dx + ….. + $\int _ { n - 1 } ^ { n } f$ (x) dx.

= (x) dx.

Hence (1) is the correct answer.