Question

Evaluate the triple integral. E (x − y) dV, where E is enclosed by the surfaces z = x2 − 1, z = 1 − x2, y = 0, and y = 4

Answer 1

The triple integral is Simplifying this is 16 times the negative number 4 over 3, which is the negative number 64 over 3.

What is the explanation?

• We have the following integrals: integral minus 1 to 1, integral 0 to 4, integral x, squared minus 1 to 1, squared minus x, minus y d, z, d y dx. Therefore, let's start by analyzing the innermost integral.
• This equates negative 1210 to 1 x, minus y times 1, minus x, squared times 2, as we have negative x, squared plus 1 dy dx.
• The 2 outside and dy dx are therefore written. In order to assess the following integral, we have two times the integral negative 1 to 11 minus x, where x is the integral and y is the integral, with lower limit 0 and upper limit 1.
• As a result, we get x minus 1 over 2 when the upper and lower bounds are substituted.
• Therefore, it is clear from this that positive 1 over 2 and negative 1 over 1 cancel each other out, as well as that negative 1 over 4 and positive 1 over 4 do as well.
• As a result, we have 16 times negative, or 2 + 2 + 3. The result of simplifying this is 16 times the negative number 4 over 3, which is the negative number 64 over 3.

To learn more about integrals refer to:

brainly.com/question/27419605

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