y = Vs2 - {-8

Q: +x-2xy) ds once around the circle x² + y² = 4, z = 0

A: ∮C(2+x−2xy)ds once around the circle x2+y2=4,z=0x2+y2=4Using parametric…

Q: 16-y2 16 – 22-y drdy by using appropriate coordinate system. an

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Q: Find the area between two curves: y=2x-x^2+3 y=x^2-4x+3 Show steps of calculation.

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Q: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

Q: y(t) +4 et"y(t – v)dv = 3. Let Y(s) denote the Laplace transform of y. (a) Apply the Laplace…

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Q: sin z dz, C (z+1)7 tan (z/2) ii) J. dz C Z-T/2

A: To Solve the above integral we use Cauchy Integral Formula.Given in Second Step.

Q: Find the area between the curve y= 2x +10 and line y4x + 16 64 64/5 64/3 O 64/7

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Q: Find the areg between Ye CosX an d y--SinX trom o tr .

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Q: Find the area between these two curves  y=x^3  &  y=x

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Q: 0.8 0.6 0.4 0.2 of -0.2 -0.4 -0.6 0.5 1.5 2 5 A direction field for y'= -(2xy2 + y³) 2.5

A: Given differential equation is: y'=-2xy2+y3. We have to sketch the direction field for the given…

Q: Write expressions for the area enclosed by a curve interms of line integrals around .

A: Green's theorem transforms the line integral around C into a double integral over the region inside…

Q: Find the area lying between the parabola y=4x - x^2 and the line y = x.

A: The given curves are y=4x-x2 and y=x. To find the area between the curves we will firstly plot these…

Q: 21.3 xdx V16 - 9х4 0.

A: We to integrate the given integration.

Q: Please find the value of integral in the image.

A: It is given that

Q: Use 8 rectangles to find the area of the curve for the equation y = -x^2 + 9 on [-3, 3].

A: area=∫abf(x)dx≈∆xf(x0)+f(x1)+...............+f(xn-2)+f(xn-1)                      where, ∆x=b-an

Q: Calculate the area between the curve y= x^3 - x^2 -2x and the lines x = - 1 x = 2 and y = 0.

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Q: Evaluate the line integral

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Q: Calculate the area of the segment cut from the curve y=x(3−x) by the line y=x. Also, sketch the…

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Q: Find the sign of the line integral.

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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.