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Question
Math
Posted 3 months ago
correct!
=210 dxx30x dy=2 \int_{-1}^{0} \mathrm{~d} x \int_{x^{3}}^{0} x \mathrm{~d} y
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Answer from Sia
Posted 3 months ago
Solution by Steps
step 1
First, we need to evaluate the inner integral with respect to y y . According to the asksia-ll calculation list, the integral of x x with respect to dy dy from x3 x^3 to 0 0 is x4 -x^4
step 2
Now, we integrate x4 -x^4 with respect to x x from 1 -1 to 0 0 . The asksia-ll calculator result for this integral is 1/5 -1/5 or 0.2 -0.2
step 3
To find the value of the double integral 210dxx30xdy 2 \int_{-1}^{0} dx \int_{x^{3}}^{0} x dy , we multiply the result from step 2 by 2 2
step 4
Multiplying 0.2 -0.2 by 2 2 gives us 0.4 -0.4
Answer
0.4 -0.4
Key Concept
Double Integration
Explanation
The double integral is evaluated by first integrating with respect to one variable and then integrating the result with respect to the other variable. In this case, we integrated with respect to y y and then with respect to x x , and finally multiplied by the constant 2 2 to get the final answer.

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