The bounds m and M used in the Bounds on an Integral Theorem for $\int _ { \frac { \pi } { 4 } } ^ { \frac { \pi } { 3 } } \sin ^ { 2 } x d x$ are

A) $\frac { 1 } { 2 } , 1$
B) $\frac { 3 } { 4 } , 1$
C) $\frac { 1 } { 2 } , \frac { 3 } { 4 }$
D) $0 , \frac { 1 } { 2 }$
E) $0 , \frac { 3 } { 4 }$

Question

The bounds m and M used in the Bounds on an Integral Theorem for $\int _ { \frac { \pi } { 4 } } ^ { \frac { \pi } { 3 } } \sin ^ { 2 } x d x$ are

A) $\frac { 1 } { 2 } , 1$
B) $\frac { 3 } { 4 } , 1$
C) $\frac { 1 } { 2 } , \frac { 3 } { 4 }$
D) $0 , \frac { 1 } { 2 }$
E) $0 , \frac { 3 } { 4 }$

Quizplus · Accepted Answer

The bounds m and M used in the Bounds on an Integral Theorem for $\int _ { \frac { \pi } { 4 } } ^ { \frac { \pi } { 3 } } \sin ^ { 2 } x d x$ are the minimum and maximum values of the function $f(x) = \sin ^ { 2 } x$ on the interval $[\frac { \pi } { 4 } , \frac { \pi } { 3 }]$. These values are $m = \frac { 1 } { 2 }$ and $M = 1$.

The Bounds M and M Used in the Bounds on an Integral