Given that ∫ {{e^{ax}}left. {dx} right|} = {a^m}{e^{ax}} + C , then which statement is

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1.Units, Dimensions and Measurement

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Given that $\int {{e^{ax}}\left. {dx} \right|} = {a^m}{e^{ax}} + C$, then which statement is incorrect (Dimension of $x = L^1$) ?

A

$m = -1$

B

Dimension of $C = L^1$

C

Dimensions of $a = L^{-1}$

D

None of these

Solution

$[ax]$ must be dimensionless, dim $[a] = L^{-1}$ ; dim $[a^me^{ax}]$ $= L$

$\Rightarrow$ dim $(a^m)$ $= L$ $\Rightarrow m = -1$, dim $[C] = L$

Standard 11

Physics

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