Write an Equivalent Double Integral with the Order of Integration $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { \sin x } ( 8 x + 9 y ) d y d x$

question 170

Multiple Choice

Write an equivalent double integral with the order of integration reversed.
- $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { \sin x } ( 8 x + 9 y ) d y d x$

• A) \(\int _ { 0 } ^ { 1 } \int _ { \pi / 2 } ^ { \sin ^ { - 1 } y } ( 8 x + 9 y ) d x d y\)
• B) \(\int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sin ^ { - 1 } y } ( 8 x + 9 y ) d x d y\)
• C) \(\int _ { 0 } ^ { 1 } \int _ { \sin ^ { - 1 } y } ^ { \pi / 2 } ( 8 x + 9 y ) d x d y\)
• D) \(\int _ { 0 } ^ { \pi / 2 } \int _ { \sin ^ { - 1 } y } ^ { 1 } ( 8 x + 9 y ) d x d y\)

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Definitions:

Major Split

A significant division or separation, often used to refer to a disagreement or divergence in a group or theory.

Archaea

A domain of single-celled microorganisms that are distinct from bacteria and eukaryotes, often found in extreme environments.

Mitochondria

Organelles found in the cells of nearly all eukaryotic organisms, responsible for producing energy through the process of oxidative phosphorylation.