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Hunter-Best [27]
3 years ago
5

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

Mathematics
1 answer:
gogolik [260]3 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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At the sewing store, Eva bought a bag of mixed buttons. She got 64 large buttons and 16 small buttons. What percentage of the bu
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Answer:

80% of the buttons were large.

Step-by-step explanation:

Recall that percentages are fractions.

We first need to find the total number of buttons that Eva bought

64 + 16 = 80

Then we need to divide 64 into 80 as a fraction of the whole (80 is our whole)

64 ÷ 80 = 0.8

To convert our decimal to a percentage, we must multiply it by 100.

0.8 * 100% = 80%

Therefore, 80% of the buttons were large.

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Standard form =
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