Consider the line integral I = O rydy – y dx where C is the square cut from the first quadrant by the lines r =1 and y = 1. (i) Find the line integral I using the circulation form of Green's Theorem. (ii) Find the line integral I using the flux form of Green's Theorem.

Q: Q5: A) Evaluate the following integral : S(z? – z-2)² + 4 dz B) Find the slope of the line tangent…

A: To evaluate the integral, the function z2-z-22+4 has to be first simplified. Now, z-2 can be…

Q: c.rechudu = 2 tan -I eu tc C. %3D

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A: To evaluate the integration

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A:

Q: c) Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d i) EevEdt dx dx J…

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Q: c) Find the value of (Log:)² where the integral is along a contour not intersecting the branch cut…

A: We find value of given contour.

Q: 1. Fill in the blank with the appropriate integration rule (You do not need to name it): Je"dr =…

A: To find the following

Q: Find cosh a In(sinh r)dr.

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A: Let's set up some notation for the problem ,  t = time measured  x(t) = distance the snowplow has…

Q: Use the given substitution to evaluate the integral.

A: Given integral: ∫sec22θ tan2θ dθ

Q: | 2°+Idal Vx² +1 dxl

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Q: de Use contour integration to evaluate the real definite integral 17- 8сos(®

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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.