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Chapter 5: Q8P (page 247)

Question: , where A is the area enclosed by the curves y = sinx, the x axis, and the line

Short Answer

Expert verified

The required solution is

Step by step solution

Definition of double integral

The double integral f(x,y)over the areaA in the (x,y)plane is the limit of this sum, and we write it as

Drawing the area bounded by the curve

The area is bounded by the curve x-axis.

Calculation of the area enclosed by the curve

Integrating the problem

Therefore, the value is

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Most popular questions from this chapter

Find the centroid of the first quadrant part of the arc $x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}$ . Hint: Let $x = a \cos 3 θ, y = a \sin 3 θ$ .

Question: A partially silvered mirror covers the square area with vertices at $(\pm 1, \pm 1)$ . The fraction of incident light which it reflects at (x, y) is $\frac{{(x - y)}^{2}}{4}$ . Assuming a uniform intensity of incident light, find the fraction reflected.

(a) Find the area of the surface $z = 1 + x^{2} + y^{2}$ inside the cylinder $x^{2} + y^{2} = 1$

(b) Find the volume inside the cylinder between the surface and the $(x, y)$ plane. Use cylindrical coordinates

Let the solid in Problem 7 have density $= c o s θ$ .

Show that then $I_{z} = \frac{3}{10} M a^{2} s i n^{2} α$ .

Under the surface z = 1 /(y+2) , and over the area bounded by and y=x $y^{2} + x = 2$ .

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Question: , where A is the area enclosed by the curves y = sinx, the x axis, and the line

Short Answer

Step by step solution

Definition of double integral

Drawing the area bounded by the curve

Calculation of the area enclosed by the curve

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Most popular questions from this chapter

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