Chapter 5: Q6P (page 247)

$\int_{y - 1}^{2} \int_{x - \sqrt{y}}^{y^{2}} x d x d y$

Short Answer

Expert verified

The required solution is $\int_{y - 1}^{2} \int_{x - \sqrt{y}}^{y^{2}} xdxdy \frac{47}{20}$ .

Step by step solution

Definition of Definite Integral

The antiderivative and indefinite integrals of a function are closely connected to the definite integral. The indefinite integral, if it exists, has a real numerical value, whereas the latter two represent an unlimited number of functions that differ only by a constant.

Finding the Integral

Consider the given integral,

$\int_{y - 1}^{2} \int_{x - \sqrt{y}}^{y^{2}} xdxdy = \int_{y - 1}^{2} [\frac{1}{2} x^{2}_{\sqrt{y}}^{y^{2}}] d y = \frac{1}{2} \int_{1}^{2} (y^{4} - y) d y = \frac{1}{10} y^{5}_{1}^{2} - \frac{1}{4} y^{2}_{1}^{2} = \frac{1}{10} (32 - 1) - \frac{1}{4} (4 - 1) = \frac{62}{10} - \frac{15}{20} = \frac{47}{20}$

Therefore, the solution is $\int_{y - 1}^{2} \int_{x - \sqrt{y}}^{y^{2}} xdxdy = \frac{47}{20}$ .

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$\int_{y - 1}^{2} \int_{x - \sqrt{y}}^{y^{2}} x d x d y$

Short Answer

Step by step solution

Definition of Definite Integral

Finding the Integral

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∫y-12∫x-yy2xdxdy

Short Answer

Step by step solution

Definition of Definite Integral

Finding the Integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physical Quantities And Units

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Study anywhere. Anytime. Across all devices.

$\int_{y - 1}^{2} \int_{x - \sqrt{y}}^{y^{2}} x d x d y$