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earnstyle [38]
2 years ago
7

Which definite integral approximation formula is the integral from a to b of f of x, dx is approximately equal to the product of

the quantity b minus a over n and the quantity y sub 0 plus y sub 1 plus y sub 2 plus y sub 3 plus dot dot dot plus y sub n minus 1?
Mathematics
2 answers:
Alexxandr [17]2 years ago
8 0

That is a description of the formula for the rectangle rule using left endpoints.

andriy [413]2 years ago
7 0

Answer:

Step-by-step explanation:

Given that integral approximation formula is calculated as follows:

Integral from a to be of f(x) dx is calculated as dividing the region between the curve, the x axis and y=a and y=b into a number of trapeziums (n) of equal width and then calculating the area of the trapeziums and adding.

The width of triangle would be (b-a)/n

The length would vary depending on the position of x.

First rectangle has length = y_0 = f(a)

Hence left end points are used

So this is Riemann left sum approximation.

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7y+4x

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Help please ty ty Appreciate it
MAVERICK [17]

Answer:

a. 113.1 cm^3.

b. 339.29 cm^3.

c. 18 cm.

d. 508.94 cm^3.

e. 169.65 cm^3.

Step-by-step explanation:

a. (4/3) * pi * (3^3) = (4/3) * pi * 27 = 36 * pi = 113.0973355, which is about 113.1 cm^{3}.

b. 113.0973355 * 3 = 339.2920066, which is about 339.29 cm^3.

c. Since the radius of a tennis ball is 3 cm, the diameter is 6 cm. There are three tennis balls, and the diameters added up become the height of the cylinder. 6 + 6 + 6 = 18 cm.

d. pi * (3^2) * 18 = pi * 9 * 18 = pi * 162 = 508.9380099, which is about 508.94 cm^3.

e. 508.9380099 - 339.2920066 = 169.6460033, which is about 169.65 cm^3.

Hope this helps!!

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