Write an Equivalent Double Integral with the Order of Integration $\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \tan ^ { - 1 } x } d y d x$

question 67

Multiple Choice

Write an equivalent double integral with the order of integration reversed.
- $\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \tan ^ { - 1 } x } d y d x$

• A) \(\int _ { 0 } ^ { \pi / 4 } \int _ { \tan y } ^ { \pi / 2 } d x d y\)
• B) \(\int _ { 0 } ^ { \pi / 4 } \int _ { \tan ^ { - 1 } y } ^ { \pi / 2 } d x d y\)
• C) \(\int _ { 0 } ^ { \pi / 4 } \int _ { \tan y } ^ { 1 } d x d y\)
• D) \(\int _ { 0 } ^ { \pi / 4 } \int _ { \tan ^ { - 1 } y } ^ { 1 } d x d y\)

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Definitions:

Psychosocial Stages

Erikson's theory that proposes eight stages of human development, each characterized by a different conflict that must be resolved for healthy psychological development.

Preschool Years

The period in a child's life prior to attending kindergarten, typically from ages 3 to 5, marked by rapid growth and development in various areas.

Human Development

A multidisciplinary field studying changes in human beings over the course of their life, including physical, cognitive, and social growth.

Erikson's Emphasis

Focus on the developmental stages of the human lifespan, proposing that individuals go through eight stages of psychosocial development from infancy to late adulthood.