In whatever way you see fit, evaluate the line integral L(10xy-3y+21x dx+ (15xy=+6xyz*)dy+ (15xy=' +9xy°=" +14x*z}dz from point (0,0,0) to point (1,1,1)

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Q: e) S(secx + cotx)* dx 2.

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Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Given: ∫(1,0,0)(0,1,1)sinycosxdx + cosysinxdy+dz To Show: (a). Differential forms in the integral…

Q: Find the complete integral of 1 dz z dx 1 dz z dx2 1 dz = x1 X2 X3. z dxz %3D

A: Given 1z∂z∂x11z∂z∂x21z∂z∂x3=x1x2x3. Find the complete integral using the Jacobi method.

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Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: To Determine: show that the differential forms in the integrals are exact. Then evaluate the…

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Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Find the complete integral of 1 dz z dx 1 dz z dxz 1 dz =x1 X2 X3. Exe z

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Q: x dy - yz dz where C is the line segment from (4, -1, 2) to (1, 7, –1).

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Q: Find the complete integral of 1 az z dx, 1 dz z dxz 1 dz =x1 x2 X3. z dxz

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A: Given Line Integral is ∮x4dx+xydy , where C is a triangle with vertices at (0,0), (0,6) and (6,0)…

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Q: Find the complete integral of 1 dz 1 dz 1 dz z dxz Ixe z z dx2 = x1 X2 X3.

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Q: Set up an iterated triple integral equal to √3-x² | = • S√³/3 SO √√3 x² + y² 3 2-₁/4-x²-y² 2y dz dy…

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Q: TRUE OR FALSE? The given line integral is independant of path.

A: The given line integral is ∫C2xz3+6ydx+6x-2yzdy+3x2z2-y2dz Compare the above line integral with…

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A: Given that Take, Now, so, Then then by comparing

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Q: Calculate the double integral. Te 1+ xy бх dA, R = [0, 6] × [0, 1] 1 + xy

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Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. Lv - x) dx +…

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A: Given : ∫( 0 , 0 ,0)( 1, 2, 3)  3 x2y dx + ( x3 - z3 ) dy - 3y z2 dz

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Q: FCx) is continoos on L3,5) and S Fex) dx= 5 Evaluate 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.