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VladimirAG [237]
2 years ago
7

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

Mathematics
1 answer:
Anettt [7]2 years ago
8 0
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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AnnZ [28]

Answer:

A

Step-by-step explanation:

There are two ways you could do this question. You could graph it with something like Desmos or you could put a couple of x values in for f(x). I'll do the latter first. When you understand it, try putting it into Desmos.

f(x) = (3/4)^x

f(0) = (3/4)^0

f(0) = 1  

=======

f(x) = (3/4)^x

f(1) = 3/4

=========

g(x) = (3/4)^x - 6

g(0) = (3/4)^0 - 6

g(0) = 1 - 6

g(0) = - 5

========

g(x) = (3/4)^x - 6

g(1) =  (3/4)^1 - 6

g(1)= 3/4 - 6

g(1) = -5 1/4

Conclusion

It looks like the graph has shifted down 6.

Answer

A

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2 years ago
Pl help it’s for a grade I will give you Brainly if right
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15ℎ2+26ℎ−21

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2 years ago
Triangle pqr is a right triangle. what is the best approximation of the length of segment pq? (Note:tan76°)
andrew11 [14]

Answer:

PQ = 16.04cm

Step-by-step explanation:

θ = 76°

QR = 4cm

PQ = ?

Since it's a right angle triangle,

QR = adjacent

PQ = opposite

Tanθ = opposite/adjacent

Tan76 = pq / 4

PQ = 4tan76

PQ = 4 * 4.010

PQ = 16.04cm

4 0
3 years ago
The base of a basketball goal has the shape of a rectangular pyramid. The base of the goal must be filled with sand so the goal
mart [117]

Answer:

  B.  15 ft^3

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

  V = (1/3)Bh

where B represents the area of the base, and h represents the height.

The base is apparently a rectangle, so its area is the product of its length and width:

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Then the volume is ...

  V = (1/3)(18 ft^2)(2.5 ft) = 15 ft^3

15 cubic feet of sand will be needed to fill the base.

3 0
2 years ago
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JulsSmile [24]

Answer:

Step-by-step explanation:

Let x = third side

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