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Rus_ich [418]
3 years ago
15

EXAMPLE 5 Evaluate the iterated integral 5 0 5 x sin(y2) dy dx. SOLUTION If we try to evaluate the integral as it stands, we are

faced with the task of first evaluating sin(y2) dy. But it's impossible to do so in finite terms since sin(y2) dy is not an elementary function. So we must change the order of integration. This is accomplished by first expressing the given iterated integral as a double integral. Using this equation backward, we have 5 0 5 x sin(y2) dy dx
Mathematics
1 answer:
Dimas [21]3 years ago
6 0

\displaystyle\int_0^5\int_x^5\sin(y^2)\,\mathrm dy\,\mathrm dx

The integration region is the triangle in the x,y plane bounded by the lines y=5, y=x, and x=0. Reversing the order of integration, this is equal to

\displaystyle\int_0^5\int_0^y\sin(y^2)\,\mathrm dx\,\mathrm dy=\int_0^5y\sin(y^2)\,\mathrm dy

For the remaining integral, let u=y^2\implies\mathrm du=2y\,\mathrm dy:

\displaystyle\int_0^5y\sin(y^2)\,\mathrm dy=\frac12\int_0^{25}\sin u\,\mathrm du=-\frac12\cos u\bigg|_0^{25}=\frac{1-\cos(25)}2

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0.135 written as a fraction is _____.<br><br><br><br> 5/37<br><br> 27/100<br><br> 27/200
sergij07 [2.7K]
First it would be 135/1000. Then you'd have to simplify.

Simplified, it would be 27/200.
4 0
3 years ago
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Haven't run across one with three terms. help? preferably explain how you got the answer too!!​
const2013 [10]

Answer:

c^3 + c^2 - 7c + 20

Step-by-step explanation:

First, expand the expression using distributive property.

c^2(c+4) - 3c(c+4) + 5(c+4)

c^3 + 4c^2 - 3c^2 - 12c + 5c + 20

Lastly, simplify like terms.

c^3 + c^2 - 7c + 20

5 0
3 years ago
A chemical company makes two brands of antifreeze. The first brand is 65% pure antifreeze, and the second brand is 90% pure anti
Murrr4er [49]

With amounts measured in gallons, let

x = amount of 65% antifreeze

y = amount of 90% antifreeze

1 gal of the 65% brand contains 0.65 gal of pure antifreeze; x gal would contain 0.65x gal. Similarly, y gal of the 90% brand contains 0.90y gal of pure antifreeze.

To obtain 120 gal of 80% antifreeze solution (which contains 0.80•120 = 96 gal of pure antifreeze), we must have

x + y = 120 … … … … … [total volume of antifreeze solution]

0.65x + 0.90y = 96 … [total volume of pure antifreeze]

Solve the first equation for y :

y = 120 - x

Substitute this into the second equation and solve for x :

0.65x + 0.90 (120 - x) = 96

0.65x + 108 - 0.90x = 96

0.25x = 12

x = 48

Solve for y :

y = 120 - 48

y = 72

6 0
2 years ago
I need help with this please
natka813 [3]

Answer:

Step-by-step explanation:

Antelope, Montana:  

    21, 30, 42, 58, 70, 79

Range- 58     79-21= 58

Quartile 1- 30

Quartile 3- 70

Interquartile Range- 40     70-30= 40

Augusta, Maine:

    28, 32, 41, 53, 66, 75

Range- 47

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3 0
3 years ago
Y=-3x+3<br> Y=5x+19<br> Solve this system by substitution
Mars2501 [29]

Answer:

x=-2

Step-by-step explanation:

You can substitute the first equation into the second:

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Add 3x on both sides:

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Subtract 19 on both sides:

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Divide 8 on both sides:

x=-2

5 0
3 years ago
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