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3 years ago

CAN SOMEONE PLEASE JUST ANSWER THIS ASAP FOR BRAINLIEST!!!

Mathematics

1 answer:

BARSIC [14]3 years ago

5 0

Answer:

F=7xy²

Step-by-step explanation:

Rewrite the question

4xy * F = 28x^2y^3 Divide by 4xy

$\Text{F = }\dfrac{28x^2y^3}{4xy}$

Divide the 4 into the 28.

Divide the x into the x^2

Divide the y into the y^3

$\Text{F=}\dfrac{7x * x * y * y * y}{4xy}$

$\Text{F=}7*x*y*y$

$\Text{F=}7*x*y^2$

F = 7xy²

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with a Riemann sum, which comes in the form

$\displaystyle\int_a^b f(x)\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^nf(x_i)\Delta x_i$

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So if we had $n=4$ subintervals, we'd split up the interval of integration as

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Note that the right endpoints follow a precise pattern of

$2=1+\dfrac44$
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$4=1+\dfrac{12}4$
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The height of each rectangle is then given by the values above getting squared (since $f(x)=x^2$ ). So continuing with the example of $n=4$ , the Riemann sum would be

$\displaystyle\sum_{i=1}^4\left(1+\dfrac{4i}4\right)^2\dfrac44$

For $n=5$ ,

$\displaystyle\sum_{i=1}^5\left(1+\dfrac{4i}5\right)^2\dfrac45$

and so on, so that the definite integral is given exactly by the infinite sum

$\displaystyle\lim_{n\to\infty}\sum_{i=1}^n\left(1+\dfrac{4i}n\right)^2\dfrac4n$