Question

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

Answer 1

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

$\text { (taking Strip as shown). }$

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

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

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

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.

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