Question

Math

Posted 3 months ago

correct！

`$=2 \int_{-1}^{0} \mathrm{~d} x \int_{x^{3}}^{0} x \mathrm{~d} y$`

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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 $y$. According to the asksia-ll calculation list, the integral of $x$ with respect to $dy$ from $x^3$ to $0$ is $-x^4$

step 2

Now, we integrate $-x^4$ with respect to $x$ from $-1$ to $0$. The asksia-ll calculator result for this integral is $-1/5$ or $-0.2$

step 3

To find the value of the double integral $2 \int_{-1}^{0} dx \int_{x^{3}}^{0} x dy$, we multiply the result from step 2 by $2$

step 4

Multiplying $-0.2$ by $2$ gives us $-0.4$

Answer

$-0.4$

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 $y$ and then with respect to $x$, and finally multiplied by the constant $2$ to get the final answer.

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