Set up only! Do not evaluate the integral. Evaluate using an appropriate change of variables: |L. I+ 2y , cos cos (r - y) - y = 0, r-y=-1, r + 2y = 0 and r+2y 2. dA , where R is the parallelogram bounded by the lines

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: Evaluate (₁ F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

A: NOTE: Refresh your page if you can't see any equations. . C:=smooth curve form (-5,4) to (3,2)…

Q: The length of the curve y = 3 - 4Vx for 0 < x < 3 is calculated by the integral: %3D Select one: 3 O…

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Q: Evaluate the line integral feF. dr where F = (4 sin x, -3 cos y, 5xz) and C is the path given by…

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Q: 4 sin 3y–6 dy cos 3y

A: We'll evaluate the integral as following.

Q: Evaluate the integral. (tant 6t dt tan 6t - tan-6 + 1 tan-6t + 36 tan 6t + t + C 18 1 tan 6t + 18…

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Q: Without evaluating the integral, show that √ √ 2 ² 4+1 4₂ | 15 | 1/2 dz where C is the line segment…

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Q: [[(2x + y²) da + 2xy dy], where C is the line segment from (-1,0) to (1, 2) Evaluate in two…

A: The line integral ∫CMdx+Ndy involves the integration over a specific path. In this case, the line…

Q: 5. True or False? The work done by a force field F on an object moving along a path C is F. dr. (a)…

A: I am only providing the solution of question (5)   as there is no question (6) in the image.

Q: - Integrate the function f orgy) =y-Vx over triangle cut from the first quadrant by Line X+y=1

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Q: sec² x dx 1– 16 tan? x

A: Consider the integration: ∫sec2x1-16tan2xdx…

Q: Ir th line x=4+2t, ーも paralled to the plone 3x +ry +2=7-

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Q: Use the given substitution to evaluate the integral.

A: Given integral: ∫sec22θ tan2θ dθ

Q: dx 8. Evaluate the integral: J x2 Vx2-16 Vx²+16 a. +C 16x Vx2-16 b. 8x Vx2 -16 ++ C. 16x 1 d. –Vx2 –…

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Q: Q4. a) Evaluate the following integral: 3 sin(5x? + 5y²) dA where Ris the region in the first…

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

A: Line integral will be path independent if vector field whose integral we need  is conservative…

Q: Integrate: S dx 5+ x2 5x

A:

Q: Evaluate This Integral if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to…

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Q: Obtain the integrating factor of the non-exact DE, (2 + ycosx)dx + xcosxdy = 0. a. secx b. cosx c…

A: Integrating factor

Q: Consider the function f (x) = cos (2x) a) Find the polynomial of degree 4 centered at X = 1.…

A: The given function is fx=cos2x

Q: Evaluate the indicated line integrals in the complex plane by direct integration. Siz dz along the…

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Q: * J²Z d²z дуг dx²² 1 = tan ³x tany - tanxton³y

A: Given that  ∂2z∂x2-∂2z∂y2=tan3xtany-tanxtan3y

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.