Question
The area bounded by the curve $$f\left( x \right) = c{e^x}\left( {c > 0} \right),$$ the $$x$$-axis and the two ordinates $$x=p$$ and $$x=q$$ is proportional to :
A.
$$f\left( p \right).f\left( q \right)$$
B.
$$\left| {f\left( p \right) - f\left( q \right)} \right|$$
C.
$$f\left( p \right) + f\left( q \right)$$
D.
$$\sqrt {f\left( p \right)f\left( q \right)} $$
Answer :
$$\left| {f\left( p \right) - f\left( q \right)} \right|$$
Solution :
$${\text{Area}} = \int_q^p {c{e^x}dx} = \left[ {c{e^x}} \right]_q^p = c\left( {{e^p} - {e^q}} \right) = f\left( p \right) - f\left( q \right)$$
$${\text{Area}} = \int_q^p {c{e^x}dx} = \left[ {c{e^x}} \right]_q^p = c\left( {{e^p} - {e^q}} \right) = f\left( p \right) - f\left( q \right)$$