Evaluate the Integral by Changing the Order of Integration in an Appropriate

question 350

Multiple Choice

Evaluate the integral by changing the order of integration in an appropriate way.
- $$\int _ { 0 } ^ { \infty } \int _ { 0 } ^ { 21 } \int _ { y / 3 } ^ { 7 } e ^ { - \left( x ^ { 2 } + z \right) } d x d y d z$$

• A) \(\frac { 3 } { 4 } \left( 1 - e ^ { - 56 } \right)\)
• B) \(\frac { 3 } { 4 } \left( 1 - \mathrm { e } ^ { - 49 } \right)\)
• C) \(\frac { 3 } { 2 } \left( 1 - \mathrm { e } ^ { - 49 } \right)\)
• D) \(\frac { 3 } { 2 } \left( 1 - e ^ { - 56 } \right)\)

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