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

question 65

Multiple Choice

Use the following property of the definite integral to estimate the definite integral $\int _ { x / 6 } ^ { s / 4 } 6 \sin x d x$ : 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)
• \(\frac { \pi } { 2 } \leq \int _ { x / 6 } ^ { x / 4 } 6 \sin x d x \leq \frac { \sqrt { 2 } \pi } { 2 }\)
• B) \(\frac { \sqrt { 2 } \pi } { 4 } \leq \int _ { x / 6 } ^ { z / 4 } 6 \sin x d x \leq \frac { \pi } { 4 }\)
• C)
• \(\frac { \pi } { 4 } \leq \int _ { x / 6 } ^ { \pi / 4 } 6 \sin x d x \leq \frac { \sqrt { 2 } \pi } { 4 }\)
• D) \(\frac { \sqrt { 2 } \pi } { 2 } \leq \int _ { z / 6 } ^ { z / 4 } 6 \sin x d x \leq \frac { \pi } { 2 }\)

Recognize the role of intuition in decision making and problem solving.

Learn about various cognitive biases and their effects on perception and judgment.

Understand the components and significance of creativity, as identified by psychologists.

Gain knowledge about animal cognition, including tool use, self-awareness, and cultural transmission among nonhuman animals.

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