Don't just guess if you don't know. I need the exact answer please

Mathematics

2 answers:

Arada [10]2 years ago

6 0

You should learn how to do this

20.5

kiruha [24]2 years ago

4 0

It would be 20.3 because if you put the numbers in order from least to greatest then you have to find the middle number and since their are 2 of them you add then divide by 2

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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

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2 years ago

What is the slope of the line that passes through the points (-3, 5) and (1, 15)

meriva

5/2 is the slope of the line

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2 years ago

Read 2 more answers

I need help!!!! Can anyone answer as fast as they can???

Morgarella [4.7K]

X= 180
now you have to multiply all them with 180
5(180)= 900
2(180)= 360

8 0