Let $$\int_a^b {f\left( x \right)dx = p} $$ and $$\int_a^b {\left| {f\left( x \right)} \right|dx = q.} $$ Then :
A.
$$\left| p \right| \leqslant q$$
B.
$$p > q$$
C.
$$p + q = 0$$
D.
none of these
Answer :
$$\left| p \right| \leqslant q$$
Solution :
Use the property $$\left| {\int_a^b {f\left( x \right)dx} } \right| \leqslant \int_a^b {\left| {f\left( x \right)} \right|dx.} $$
Releted MCQ Question on Calculus >> Application of Integration
Releted Question 1
The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-