int_{0}^{2} int_{x}^{2} 2 y^{2} sin (x y) d y d x

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Accepted Answer

Step:1 ：First, we compute the inner integral, treating x as a constant. The inner integral is (int_{x}^{2} 2 y^{2} sin (x y) d y).Step:2 ：Next, we substitute the limits of integration for y, which are x and 2.Step:3 ：Then, we compute the outer integral, which is (int_{0}^{2} text{{inner integral}} d x).Step:4 ：We substitute the limits of integration for x, which are 0 and 2.Step:5 ：Finally, we simplify the result to get the final answer.Step:6 ：The final answer is (boxed{4 - sin(4)}).

Answer

Step: 1 ：First, we compute the inner integral, treating x as a constant. The inner integral is (int_{x}^{2} 2 y^{2} sin (x y) d y).Step: 2 ：Next, we substitute the limits of integration for y, which are x and 2.Step: 3 ：Then, we compute the outer integral, which is (int_{0}^{2} text{{inner integral}} d x).Step: 4 ：We substitute the limits of integration for x, which are 0 and 2.Step: 5 ：Finally, we simplify the result to get the final answer.Step: 6 ：The final answer is (boxed{4 - sin(4)}).

$\int_{0}^{2} \int_{x}^{2} 2 y^{2} \sin (x y) d y d x$

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$\int_{0}^{2} \int_{x}^{2} 2 y^{2} \sin (x y) d y d x$