Parle to Fully demonstrate eva luate the Integral Litegration by demonst ra te 3メ 5xe

Q: b) Express the area of the pool, A in terms of I and r. c) Hence, or otherwise show that A = -² +…

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Q: dy Use dsolve to solve dt 3D 5у — 5ty³

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Q: -1 0. +6 -4 -3

A: Just I have used the rule of scalar multiplication to a matrix and addition of two matrices and at…

Q: Find the arclength of y = 2a + 4 on 0 < a < 4

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Q: TT Evaluate A eit dt 4 0.

A: This problem can be solved easily by the substitution method.

Q: Q3) Use substitution to find the following integrals a. f sec²x √tan x dx b. dx x3 Sa (1+x4)5 C. csc…

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Q: Evaluate |- 1 =dx. a) xVx* +1

A: Given: ∫1xx4+1dx

Q: (3X dx =? Sinmply

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Q: Find the fluid force (in lb) on a circular observation window of radius 1 foot in a vertical wall of…

A: Solution is uploaded below.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.