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Bess [88]
3 years ago
15

Express the given integral as the limit of a riemann sum but do not evaluate: the integral from 0 to 3 of the quantity x cubed m

inus 6 times x, dx.
Mathematics
1 answer:
WARRIOR [948]3 years ago
4 0
We will use the right Riemann sum. We can break this integral in two parts.
\int_{0}^{3} (x^3-6x) dx=\int_{0}^{3} x^3 dx-6\int_{0}^{3} x dx
We take the interval and we divide it n times:
\Delta x=\frac{b-a}{n}=\frac{3}{n}
The area of the i-th rectangle in the right Riemann sum is:
A_i=\Delta xf(a+i\Delta x)=\Delta x f(i\Delta x)
For the first part of our integral we have:
A_i=\Delta x(i\Delta x)^3=(\Delta x)^4 i^3
For the second part we have:
A_i=-6\Delta x(i\Delta x)=-6(\Delta x)^2i
We can now put it all together:
\sum_{i=1}^{i=n} [(\Delta x)^4 i^3-6(\Delta x)^2i]\\\sum_{i=1}^{i=n}[ (\frac{3}{n})^4 i^3-6(\frac{3}{n})^2i]\\
\sum_{i=1}^{i=n}(\frac{3}{n})^2i[(\frac{3}{n})^2 i^2-6]
We can also write n-th partial sum:
S_n=(\frac{3}{n})^4\cdot \frac{(n^2+n)^2}{4} -6(\frac{3}{n})^2\cdot \frac{n^2+n}{2}

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GalinKa [24]

Answer:

ASA RULE

Step-by-step explanation:

As 2 angles are given and RV is common in both trianlges hence TVR is congruent to SRV by ASA rule

7 0
3 years ago
It took the race car 22 minutes to travel 114.4 kilometers. At what rate did the car travel?Use the formula r = d/t, where r is
kramer
D=114.4 kilometers
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3 0
3 years ago
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The sum of two consecutive cube numbers is 341. Work out the two numbers. (2 marks)
Kobotan [32]

Answer:

63 and 53

Step-by-step explanation:

you could use trail and error. So:

13+23=9

33+43=91

63+73=559

53+63=341

3 0
3 years ago
Min is about to roll a six-sided number cube. What is the probability that she will roll an even number? A) 1 4 B) 1 3 C) 1 2 D)
Irina-Kira [14]
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8 0
3 years ago
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Read the ques
Dafna11 [192]

Answer:

0.25feet

Step-by-step explanation:

The equation is not well written. Let the equation of the height be modelled as;

h = -16d²+8d+4

The velocity of the ball is zero at its maximum height.

Velocity = change in displacement/time

v = dh/dd

Differentiate

v = -32d+8

Since dh/dd = v = 0

0 = -32d+8

Add 32d to both sides

0+32d = 8

32d = 8

Divide both sides by 32

32d/32 = 8/32

d = 1/4

d = 0.25feet

Hence the maximum height of the tennis ball is 0.25feet

Note that the modeled equation was assumed. You can apply the same calculation to any equation given

3 0
3 years ago
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