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3 years ago

U=\frac{a\pih^2a}{m} \int\limits^a_b {x} \, dx \pi d^3 x l w (x) l^4 evaluate it

Mathematics

1 answer:

blsea [12.9K]3 years ago

8 0

I'm interested in integrals of the form

I(a,b)=∫

∞

arccot(x)⋅arccot(ax)⋅arccot(bx) dx, for a>0,b>0

It's known†Gradshteyn & Ryzhik, Table of Integrals, Series, and Products, 7th edition, page 599, (4.511) that

I(a,0)=

π2

[ln(1+

ln(1+a)

Maple and Mathematica are also able to evaluate

I(1,1)=

3π2

ln2−

ζ(3).

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Answer:

18.02 cm

Step-by-step explanation:

A diagonal makes a rectangle into two right triangles. So if we use the Pythagorean theorem we can find the hypotenuse which is the diagonals.

Remember, because we know the length and width, we know the two sides.

10^2 + 15^2 = c^2

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3 years ago

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grin007 [14]

we have

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11 months ago

Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ? triangles WXZ and XYZ that share side XZ with right an

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2 years ago

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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Darina [25.2K]

Answer:

Given definite integral as a limit of Riemann sums is:

$\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

Step-by-step explanation:

Given definite integral is:

$\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}$

Substituting (2) in above

$f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

Riemann sum is:

$= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

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