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Shtirlitz [24]
3 years ago
7

I need help ASAP Please and thanks

Mathematics
2 answers:
pishuonlain [190]3 years ago
8 0
It’s the 3rd one hope this helps
Leokris [45]3 years ago
3 0

Answer:its number 3

Step-by-step explanation:

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Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
Otrada [13]

I guess the "5" is supposed to represent the integral sign?

I=\displaystyle\int_1^4\ln t\,\mathrm dt

With n=10 subintervals, we split up the domain of integration as

[1, 13/10], [13/10, 8/5], [8/5, 19/10], ... , [37/10, 4]

For each rule, it will help to have a sequence that determines the end points of each subinterval. This is easily, since they form arithmetic sequences. Left endpoints are generated according to

\ell_i=1+\dfrac{3(i-1)}{10}

and right endpoints are given by

r_i=1+\dfrac{3i}{10}

where 1\le i\le10.

a. For the trapezoidal rule, we approximate the area under the curve over each subinterval with the area of a trapezoid with "height" equal to the length of each subinterval, \dfrac{4-1}{10}=\dfrac3{10}, and "bases" equal to the values of \ln t at both endpoints of each subinterval. The area of the trapezoid over the i-th subinterval is

\dfrac{\ln\ell_i+\ln r_i}2\dfrac3{10}=\dfrac3{20}\ln(ell_ir_i)

Then the integral is approximately

I\approx\displaystyle\sum_{i=1}^{10}\frac3{20}\ln(\ell_ir_i)\approx\boxed{2.540}

b. For the midpoint rule, we take the rectangle over each subinterval with base length equal to the length of each subinterval and height equal to the value of \ln t at the average of the subinterval's endpoints, \dfrac{\ell_i+r_i}2. The area of the rectangle over the i-th subinterval is then

\ln\left(\dfrac{\ell_i+r_i}2\right)\dfrac3{10}

so the integral is approximately

I\approx\displaystyle\sum_{i=1}^{10}\frac3{10}\ln\left(\dfrac{\ell_i+r_i}2\right)\approx\boxed{2.548}

c. For Simpson's rule, we find a quadratic interpolation of \ln t over each subinterval given by

P(t_i)=\ln\ell_i\dfrac{(t-m_i)(t-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+\ln m_i\dfrac{(t-\ell_i)(t-r_i)}{(m_i-\ell_i)(m_i-r_i)}+\ln r_i\dfrac{(t-\ell_i)(t-m_i)}{(r_i-\ell_i)(r_i-m_i)}

where m_i is the midpoint of the i-th subinterval,

m_i=\dfrac{\ell_i+r_i}2

Then the integral I is equal to the sum of the integrals of each interpolation over the corresponding i-th subinterval.

I\approx\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt

It's easy to show that

\displaystyle\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt=\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)

so that the value of the overall integral is approximately

I\approx\displaystyle\sum_{i=1}^{10}\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)\approx\boxed{2.545}

4 0
3 years ago
Eighty, decreased by three times a
Marina86 [1]

Answer:

The number is 9.

Step-by-step explanation:

Lets write this as an equation first. We'll substitute the number for the variable <em>x</em>.

80 - 3x = 5x + 8

First, let's add 3x to both sides.

80 - 3x + 3x = 5x + 3x + 8

80 = 8x + 8

Next, let's subtract 8 from both sides.

80 - 8 = 8x + 8 - 8

72 = 8x

Finally, let's divide both sides by 8.

72/8 = 8x/8

9 = x

<em>"x" is 9.</em>

<em>So the secret number is 9.</em>

P.S.

This is my first answer to a Brainly question so please don't complain!

6 0
2 years ago
A new drug claims to reduce the number of migraines an individual suffers. In a study on the effectiveness of the new drug, 50 s
lana66690 [7]

Answer:

I got A on edg

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Rewrite 2/7 and 1/4 so they have a common denominator
Zolol [24]
I think it’s 2/7=8/28 1/4=7/28
8 0
2 years ago
Need answer quick please answer
lisov135 [29]

Answer: 24.96

Step-by-step explanation: just multiply them together

8 0
2 years ago
Read 2 more answers
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