(3ab-5a-3) - (3ab-1)

Find a closed form expression for the nth right Riemann sum of this integral?

DIA [1.3K]

Partitioning the interval $[6,11]$ into $n$ equally-spaced subintervals gives $n$ rectangles of width $\Delta x=\dfrac{11-6}n=\dfrac5n$ and of heights determined by the right endpoints of each subinterval.

If $a=x_1=6$ , then $x_2=6+\dfrac5n$ , $x_3=6+2\dfrac5n$ , and so on, up to $b=x_{n+1}=6+n\dfrac5n=11$ . Because we're using the right endpoints, the approximation will consider $x_2,\ldots,x_{n+1}$

The definite integral is then approximated by

$\displaystyle\int_6^{11}(1-5x)\,\mathrm dx\approx\sum_{i=2}^{n+1}f(x_i)\Delta x=\sum_{i=2}^{n+1}\left(1-\left(6+(i-1)\dfrac5n\right)\dfrac5n$

You have

$\displaystyle\sum_{i=2}^{n+1}\left(1-5\left(6+(i-1)\dfrac5n\right)\dfrac5n=\sum_{i=2}^{n+1}\left(-29-\dfrac{25}n(i-1)\right)\dfrac5n$
$=\displaystyle-{145}n\sum_{i=2}^{n+1}1-\dfrac{125}{n^2}\sum_{i=2}^{n+1}(i-1)$
$=-145-\dfrac{125(n^2+n)}{2n^2}$
$=-\dfrac{145}2-\dfrac{125}{2n}$

To check that this is correct, let's make sure the sum converges to the exact value of the definite integral. As $n\to\infty$ , you have the sum converging to $-\dfrac{145}2$ .

Meanwhile,

$\int_6^{11}(1-5x)\,\mathrm dx=\left[x-\dfrac52x^2\right]_{x=6}^{x=11}=-\dfrac{415}2$

so we're done.

4 0

3 years ago

8 - (-9) simplified with each expression

Arte-miy333 [17]

Hi :)

Let's remember some arithmetic w/ negative integers :

a+(-b)=a-b

a-(-b)=a-b

Now

8-(-9)=8+9=17

So the answer's 17

I hope this helps

7 0

2 years ago

How is locating -1.5 on a number line the same as locating 1.5 on a number line How is it different?

Nezavi [6.7K]

Locating -1.5 on a number line is the same as locating 1.5 because both numbers are the same distance from zero, but in opposite directions. The numbers also have the same absolute value.

Locating -1.5 and 1.5 is different because -1.5 can be found to the left of zero (because it is a negative number) while 1.5 is found to the right of zero (because it’s a positive number).

5 0

3 years ago

Match each condition to the number of quadrilaterals that can be constructed to fit the condition.

Sedbober [7]

Answer:

See the explanation.

Step-by-step explanation:

Condition A.

A rectangle with four right angles

There can be many quadrilaterals satisfying this condition.

Condition B.

A square with one side measuring 5 inches

There can be only one quadrilateral satisfying this condition.

Condition C.

A rhombus with one angle measuring 43°

There can be many quadrilaterals satisfying this condition.

Condition D.

A parallelogram with one angle measuring 32°

There can be many quadrilaterals satisfying this condition.

Condition E.

A parallelogram with one angle measuring 48° and adjacent sides measuring 6 inches and 8 inches.

There can be only one quadrilateral satisfying this condition.

Condition F.

A rectangle with adjacent sides measuring 4 inches and 3 inches.

There can be only one quadrilateral satisfying this condition.

(Answer)

5 0

3 years ago

Read 2 more answers

Determine the slope and y-intercept of the line represented by the equation:<br> 3x – 4y - 16 = 0

Diano4ka-milaya [45]

Here you are)see the attachment

8 0

3 years ago

Read 2 more answers