Question

Triple intregation Question
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Answer 1

Answer:

$\huge \pink{ \frac{175}{2} }$

Step-by-step explanation:

$\int_{ - 1} ^{ 4} \int_{0} ^{3 } \int_{1} ^{ 2} {x}^{2} y \: dx \: dy \: dz \\ \\ = \int_{ - 1} ^{ 4} \int_{0} ^{3 } [ \frac{ {x}^{3}y }{3} \big] _{1} {}^{2} \: \: dy \: dz \\ \\ = \int_{ - 1} ^{ 4} \int_{0} ^{3 } [ \frac{y}{3} ( {2}^{3} - 1) ] \: dy \: dz\\ \\ = \frac{7}{3} \int_{ - 1} ^{ 4} \int_{0} ^{3 } y \: dy \: dz \\ \\ = \frac{7}{3} \int_{ - 1} ^{4} \frac{ {4}^{2} - {1}^{2} }{2} \: dz \\ \\ = \frac{7 \times 15}{3 \times 2} \int_{ - 1} ^{4} dz \\ \\ = \frac{7 \times 15}{3 \times 2} \times \{4 - ( - 1) \} \\ \\ = \frac{175}{2}$