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Hunter-Best [27]

2 years ago

5

Evaluate the integral from negative infinity to infinity of xe^(x^(2)) dx

1 answer:

gogolik [260]2 years ago

8 0

$\int{xe^{-x^2}}dx$ <span>

Let u=-x^2
du/dx=-2x
-du/2=x dx

</span> $\int{xe^{-x^2}}dx=-1/2\int{e^u}du =- \frac{e^u}{2}+C=-\frac{e^{-x^2}}{2}+C$

<span>When x approaches infinity (or minus infinity, since it is squared), e^(-x^2) approaches zero. So the answer is zero.</span>

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14. _______________ is the opposite of 6 on the number line.

cricket20 [7]

6 is six units to the right of the 0, or zero, midpoint on an infinite number line
-6 would be six units to the left of the midpoint, so it would be the opposite

6 0

3 years ago

Read 2 more answers

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lubasha [3.4K]

Answer

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4 0

3 years ago

Four friends shared 1/2 of one carton of orange juice and 1/4 of another carton of apple juice. What fraction of each carton of

Natalka [10]

Answer:

$\dfrac{1}{16}$

$\dfrac{1}{32}$

$\dfrac{3}{32}$

Step-by-step explanation:

So in the first carton of orange juice 4 friends shared the juice.

This can be shown as:

$\dfrac{(\dfrac{1}{2})}{4}$

$\dfrac{(\dfrac{1}{2})}{4}=\dfrac{1}{16}$

The 4 friends got 1/16 of the carton each in the first carton of OJ.

Next for the second carton, it can be shown as:

$\dfrac{(\dfrac{1}{4})}{4}$

$\dfrac{(\dfrac{1}{2})}{4}=\dfrac{1}{32}$

The 4 friends got 1/32 of the carton each in the first carton of OJ.

Now to see how much they got in total each, we simply add 1/16 to 1/32

$Total OJ each = \dfrac{1}{16}+\dfrac{1}{32}$

$Total OJ each = \dfrac{3}{32}$

Each friend got a total of $\dfrac{3}{32}$ each from both cartons of OJ.

3 0

2 years ago

Need help with this question

posledela

Answer:

QR = 82.38 to nearest hundredth.

Step-by-step explanation:

As they are similar corresponding sides are in the same ratio.

So MN / QR = LM / QR

13/51 = 21/ QR

`3QR = 51*21

QR = 51*21/13

QR = 82.38

4 0

2 years ago

An experienced landscaper thought it would be funny to play a joke on some rookie landscapers. The rookies were given the measur

pashok25 [27]

Answer:

48∛9 ft²

Step-by-step explanation:

The length (L) and width (W) are given by:

$L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}$

Since this is a rectangular region, the area is given by:

$A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2$

The answer can be further simplified by factoring as follows:

$A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2$

The exact area is its simplest form is 48∛9 ft²

6 0

2 years ago