Math Problem Statement

Evaluate the following integral. Integral from 0 to StartFraction pi Over 2 EndFraction Integral from y to StartFraction pi Over 2 EndFraction 6 sine left parenthesis 2 x minus 3 y right parenthesis dx font size decreased by 5 dy Question content area bottom Part 1 Integral from 0 to StartFraction pi Over 2 EndFraction Integral from y to StartFraction pi Over 2 EndFraction 6 sine left parenthesis 2 x minus 3 y right parenthesis dx font size decreased by 5 dy equals    3 ​(Type an exact​ answer, using pi as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Double Integral
Trigonometry
Substitution
Trigonometric Identities

Formulas

∫sin(u) du = -cos(u)
cos(π - 3y) = -cos(3y)
cos(-y) = cos(y)

Theorems

Trigonometric Integration
Substitution Method for Integrals

Suitable Grade Level

College Level