Use the Following Property of the Definite Integral to Estimate $\int _ { z / 6 } ^ { \pi / 4 } 6 \sin x d x$

question 156

Multiple Choice

Use the following property of the definite integral to estimate the definite integral $\int _ { z / 6 } ^ { \pi / 4 } 6 \sin x d x$ :
If $m \leq f ( x ) \leq M$ on $[ a , b ]$ , then
$$m ( b - a ) \leq \int _ { a } ^ { b } f ( x ) d x \leq M ( b - a )$$

• A)
• \(\frac { \pi } { 2 } \leq \int _ { s / 6 } ^ { x / 4 } 6 \sin x d x \leq \frac { \sqrt { 2 } \pi } { 2 }\)
• B) \(\frac { \sqrt { 2 } \pi } { 4 } \leq \int _ { z / 6 } ^ { s / 4 } 6 \sin x d x \leq \frac { \pi } { 4 }\)
• C)
• \(\frac { \pi } { 4 } \leq \int _ { s / 6 } ^ { s / 4 } 6 \sin x d x \leq \frac { \sqrt { 2 } \pi } { 4 }\)
• D) \(\frac { \sqrt { 2 } \pi } { 2 } \leq \int _ { s / 6 } ^ { \pi / 4 } 6 \sin x d x \leq \frac { \pi } { 2 }\)

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