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Evaluate the integral by reversing the order of integration,

int_(0)^(2)int_(3y)^(6)13e^(x^(2))dxdy

Evaluate the integral by reversing the order of integration, $\newline$ $\int_{0}^{2} \int_{3 y}^{6} 13 e^{x^{2}} d x d y$

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Double integration by reversing the order

Full solution

Q. Evaluate the integral by reversing the order of integration,

\newline

\int_{0}^{2} \int_{3 y}^{6} 13 e^{x^{2}} d x d y

Understand the problem: First, we need to understand the problem. The electrician needs a total of $8,000$ centimeters of electrical tape, and each roll contains $2,000$ centimeters of tape. To find out how many rolls the electrician should order, we divide the total amount of tape needed by the amount of tape on each roll.
Calculate rolls needed: Perform the division to calculate the number of rolls needed. $8,000 \, \text{cm} \div 2,000 \, \text{cm}/\text{roll} = 4 \, \text{rolls}$
Check for errors: Check the calculation for any mathematical errors. Since $8,000$ divided by $2,000$ indeed equals $4$ , there are no errors in the calculation.

More problems from Double integration by reversing the order

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Evaluate the integral by reversing the order of integration.

\newline

\int_{0}^{\sqrt{3} \pi} \int_{y}^{\sqrt{3 \pi}} \cos \left(3 x^{2}\right) d x d y

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Question

Evaluate the integral by reversing the order of integration.

\newline

\int_{0}^{2} \int_{3 y}^{6} 13 e^{x^{2}} d x d y

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\newline

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\newline

5

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Question

10\text{-kg}

bucket is lifted from the ground to a height of

14\, \text{m}

at a constant speed with a rope that weighs

0.6\, \text{kg/m}

. Initially the bucket contains

42\, \text{kg}

of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the

14\, \text{m}

level. How much work is done? (Use

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g

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x

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x_i

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Question

10-\mathrm{kg}

bucket is lifted from the ground to a height of

14

m at a constant speed with a rope that weighs

0.6 \mathrm{~kg} / \mathrm{m}

. Initially the bucket contains

42

kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the

14-\mathrm{m}

level. How much work is done? (Use

9.8 \mathrm{~m} / \mathrm{s}^{2}

\newline

Show how to approximate the required work (in J) by a Riemann sum. (Let

x

be the height in meters above the ground. Enter

x_{i}^{* *}

x_{i}

\newline

\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(\boxed{98+35.28 x_{i}}\right) \Delta x

\newline

Express the work (in J) as an integral in terms of

x

\newline

\int_{0}^{14}(98+35.28 x

\newline

Evaluate the integral (in J). (Round your answer to the nearest integer.)

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