Show that the following line integral is path independent and evaluate its value. Show the details of your work (5.3) sinh (- (0.0) Ssinh(+X6xdx+ 10ydy) x² y2. 3

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Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: 1. What should be A for the path independent of (2,4) xy+ ^ dr + 2Ay – x dx + y? fip- (1,2) Moreover…

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Q: 1. What should be A for the path independent of (2,4) 2Ay – x dy y? XY + A dx+ (1,2) Moreover…

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A: Note:- As per your request i am solving here question no. 3 part B only.

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A: ∫1x(x+1)dx Substitute :               u = x ⇒ dudx = 12x               ⇒ dx =…

Q: 1. What should be A for the path independent of (2,4) xy + ) 2Ay – x y? (1,2) Moreover evaluate the…

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Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

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Q: 1. What should be for the path independent of (2,4) 2Ay – x dp. y? xy + A dx + (1,2) Moreover…

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Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x du -dp y? dx + (1,2) Moreover…

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Q: Evaluate the following Integrals: 1. (sin(4t) – 3 sin(2t)“ dt 6. Vsech(4x) tan (4x) dx 3 sin sinh 3y…

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – x dy. y? -dx + (1,2) Moreover…

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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.