Provide an Appropriate Response$\text { Prove that } \int _ { a } ^ { b } k r ( t ) d t = k \int _ { a } ^ { b } r ( t ) d t \text { for any scalar constant } k$

Question

Examlex · Accepted Answer

The Answer is

\begin{array}{l}\int _ { a } ^ { b } k r ( t ) d t = \int _ { a } ^ { b } k ( x ( t ) i + y ( t ) j ) d t = \int _ { a } ^ { b } k x ( t ) i + k y ( t ) j d t\= k \int _ { a } ^ { b } x ( t ) i d t + k \int _ { a } ^ { b } y ( t ) j d t = k \left[ \int _ { a } ^ { b } x ( t ) i d t + \int _ { a } ^ { b } y ( t ) j d t ight]\= k \left[ \int _ { a } ^ { b } ( x ( t ) i + y ( t ) j ) d t ight] = k \int _ { a } ^ { b } r ( t ) d t\end{array}

Provide an Appropriate Response $\text { Prove that } \int _ { a } ^ { b } k r ( t ) d t = k \int _ { a } ^ { b } r ( t ) d t \text { for any scalar constant } k$

Definitions:

Provide an Appropriate Response Prove that ∫abkr(t)dt=k∫abr(t)dt for any scalar constant k\text { Prove that } \int _ { a } ^ { b } k r ( t ) d t = k \int _ { a } ^ { b } r ( t ) d t \text { for any scalar constant } k Prove that ∫ab​kr(t)dt=k∫ab​r(t)dt for any scalar constant k

Definitions:

Provide an Appropriate Response $\text { Prove that } \int _ { a } ^ { b } k r ( t ) d t = k \int _ { a } ^ { b } r ( t ) d t \text { for any scalar constant } k$