Question

If $\frac{ d }{ dx }(\phi( x ))= f ( x )$, then $\int\limits_{1}^{2} f ( x )$ is equal to:

• A. $f(1) - f(2)$
• B. $\phi (1) - \phi (2)$
• C. $f(2) - f(1)$
• D. $\phi (2) - \phi (1)$

Answer 1

Answer: (D)

$\phi (2) - \phi (1)$

Answer 2

$\int\limits_{1}^{2} f ( x ) d x =\int\limits_{1}^{2} \frac{ d }{ dx }(\phi( x )) dx$
$\int\limits_{1}^{2} f ( x ) d x$ $=[\phi( x )]_{1}^{2}$

\int\limits_{1}^{2} f ( x ) d x$$=\phi(2)-\phi(1)

So,the correct answer is (D): ϕ(2)− ϕ(1)