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2 years ago

If y = 4 when x = -6, find y when x = 15.

Mathematics

1 answer:

SVETLANKA909090 [29]2 years ago

6 0

Y=5. Difference between -6 and 4 is ten so 15-10 =5

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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:

Fundamental Theorem of Calculus

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

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

$\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 indefinite integral:

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

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:

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

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2 years ago

Annika is very popular and tends to get bigger tips. She worked 28 hours and made an average of $14.62 per hour in a month when

aev [14]

Umm where is the ‘chart bellow’?

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3 years ago

Student to faculty is 17:3 The total is 740 how many students and faculty are at the college

inn [45]

Let the faculties be X and the number of students be Y.
X/Y = 17/3
3X= 17Y
X=17Y/3
Let that be equation 1
We also know that X+Y = 740. Let it be equation 2
Substitute equation 1 in equation 2
(17Y/3)+Y= 740
20Y/3 = 740
Y=111
Since the total is 740, then X equal 740-111 =629.
The number of faculties is 111 and the number of students is 629.

7 0

3 years ago

Read 2 more answers

What is the solution to -4|-2x+6| = -24

Arte-miy333 [17]

X = 0. Since the absolute value of -2x+6 is 2x+6, the absolute value sign acts as () so it would be -4(2x+6) = -24. That would come out to be -8x -24 = -24. Using proper algebra, the answer would come out to be 0

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Sjsjsjsjsjdjdjsjs also Ian’s lol banksia

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3 years ago