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sashaice [31]
2 years ago
12

Evaluate the following​ integral, where R is bounded by ​, ​, and . Question content area bottom Part 1 enter your response here

​(Simplify your​ answer.)
Mathematics
1 answer:
Volgvan2 years ago
7 0

\iint_{R} y^{2} d A=\int_{x=-2}^{3} \int_{y=-x-2}^{3 x+6} y^{2} d x d y d x

\text { (taking Strip as shown). }

=\int_{-2}^{3}\left(\frac{y^{3}}{3}\right)_{-x-2}^{3 x+6} d x

=\frac{1}{3} \int_{-2}^{3}(3 x+6)^{3}-(-x-2)^{3} d x

\begin{gathered}=\frac{1}{3}[4375]=\frac{4375}{3} \\=1458.33\end{gathered}

What is integral ?

  • Calculating an integral is called integration.
  • Mathematicians utilize integrals to determine a variety of useful quantities, including areas, volumes, displacement, etc.
  • When we discuss integrals, we often refer to definite integrals.
  • For antiderivatives, indefinite integrals are utilized.
  • Apart with differentiation, integration is one of the two main calculus subjects in mathematics (which measure the rate of change of any function with respect to its variables).
  • It's a broad subject that is covered in courses at the higher grade levels, such classes 11 and 12.
  • Broadly speaking, integration by parts and via substitution is explained.
  • You will discover the definition of integrals in mathematics, the integration formulae, and examples here.

So the more about integral visit.

brainly.com/question/2289273

#SPJ4

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