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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

Above the triangle with vertices (0,2),(1,1) and (2,2) , and under the surface z = xy.

Verify each of the following answers for an indefinite integral by one or more of the methods suggestedabove.

1. $\int 2 \sin θ \cos θ d θ = \sin^{2} θ$ or $- \cos^{2} θ$ or $- \frac{1}{2} \cos 2 θ$ Hint: Use trig identities.

Verify each of the following answers for an indefinite integral by one or more of the methods suggested above.

$2 . \int \frac{d x}{\sqrt{x^{2} + a^{2}}} = \sin h^{- 1} \frac{x}{a}$ or $In (x + \sqrt{x^{2} + a^{2}})$ . Hint: To find the $\sin h^{- 1}$ form, make the substitution, $x = a \sin h u$ . or see Chapter, Sections $15$ and $17$ .}

Find the volume between the planes z = 2x + 3y +6 and z = 2x + 7y + 8, and over the triangle with vertices, (0,0) (3,0) and (2,1).

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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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