Q. If $I_{1} = \int_{0}^{1}{{2^{x}}^{2}\ dx,\ I_{2} = \int_{0}^{1}{{2^{x}}^{3}\ dx,\ I_{3} = \int_{1}^{2}{2^{x}}^{2}}}\ dx\ and\ I_{4} = \int_{1}^{2}{{2^{x}}^{3}\ dx}$, then
A) $I_{3} > I_{4}$
B) $I_{3} = I_{4}$
C) $I_{1} > I_{2}$
D) $I_{2} > I_{1}$
Explanation
(c)
$\because$ $2^{x^{3}} < 2^{x^{2}},0 < x < 1\ \ \ and\ \ \ 2^{x^{3}} > 2^{x^{2}},\ \ x > 1$
$\therefore I_{4} > I_{3}\ \ \ \ and\ \ \ \ I_{2} < I_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.