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Blababa [14]
3 years ago
6

Is 68 a perfect square

Mathematics
2 answers:
AURORKA [14]3 years ago
8 0
No, because a perfect square has the volume of 24 
ziro4ka [17]3 years ago
8 0
No because a perfect square has a volume of 24
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Find integra of xlnxdx
Mademuasel [1]

Answer:

\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a <u>constant of integration</u>.

\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}

Increase the power by 1, then divide by the new power.

Given <u>indefinite integral</u>:

\displaystyle \int x \ln x \:\: \text{d}x

To integrate the given integral, use Integration by Parts:

\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}

\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}

\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2

Therefore:

\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}

Learn more about integration here:

brainly.com/question/27805589

brainly.com/question/27983581

brainly.com/question/27759474

5 0
2 years ago
Find an angle between 0 and 360 degrees that is coterminal with 232
chubhunter [2.5K]

Answer:

Hola que hace

:I

Step-by-step explanation:

4 0
2 years ago
Which two ratios form a proportion?
s2008m [1.1K]

Answer:

02:3 and 12:18

Step-by-step explanation:

A proportion is formed when the larger ratio can be simplified to equal the smaller ratio:

#1

02:3 and 4:12

Reducing the larger ratio: 4:12=1:3

Hence, not a proportion.

#2

02:3 and 6:12

Reducing the larger ratio: 6:12=1:2

Hence, not a proportion.

#3

02:3 and 12:18

Reducing the larger ratio: 12:18=2:3

Hence, they form a proportion.

#4

02:3 and 12:18

Reducing the larger ratio: 12:36=1:3

Hence, not a proportion.

4 0
3 years ago
Find the circumference of this circle please
aliya0001 [1]

The circumference equals diameter x pie which equals:

17x3.14=53.38cm.

3 0
2 years ago
A zoo measured the wingspan, in millimeters of 9 butterflies What is the median length of the wingspan
Kaylis [27]
I’m gonna say 24 mm explanation I’m guessing
7 0
2 years ago
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