Question

Assume that $\frac { 1 } { c } \int _ { a c } ^ { b c } f \left( \frac { x } { c } \right) d x =$

• A. $\int _ { a } ^ { b } f \left( \frac { x } { c } \right) d x$
• B. $\frac { 1 } { c } \int _ { a } ^ { b } f ( x ) d x$
• C. $\int _ { a } ^ { b } f ( x ) d x$
• D. None of these

Answer 1

Answer: (C)

$\int _ { a } ^ { b } f ( x ) d x$

Answer 2

$I = \frac { 1 } { c } \int _ { a c } ^ { b c } f ( x / c ) d x$

Put $\frac { x } { c } = t \Rightarrow d x = c d t$ and $x = b c \Rightarrow t = b$

$I = \int _ { a } ^ { b } f ( t ) d t = \int _ { a } ^ { b } f ( x ) d x$.