We define D = {(x, y) = R² | 0 ≤ x ≤ 1,0 ≤ y ≤ 1,x² + y² ≥ 1}. Calculate xy √√₂1 +2²2 +3²dA.

Q: 3. Evaluate || (3y+ 2x“) dA, where R = {(x, y) E R² : |x|+|y| < 1}. R.

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Q: If the substitution u = √x + 1 is made, the integral 3 A S u² u² - 1 du B du 3 2u²2 u² - 1 √ √x+1 dx…

A: We solve the given problem by using the substitution method.

Q: If 9 = {(1, y) |1 ≤ x ≤ 3,3 ≤ y ≤ 6}: D then: 11,3 dr dy

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Q: Evaluate " " So s L dz dx dy rvZ c3y (8-x²-y² Jx²+3y²

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Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: C (3y-six) dx + (7x + √y² +1) dy

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Q: Evaluate xy ds, where C is describe by æ = 4t, y= 3t, 0 <t<1. Enter your answer as a number in…

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Q: 7. Solve: dy x + 3y d.x 3x + Y

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Q: ²5° c) Evaluate x² (1 + x³)³ dx

A: We solve given integral by method of substitution.  To make integral easier,  we substitute some…

Q: 41. For ), find all values ofx and y such thatx,y)=0 simultaneously. and yr.y)=0 f(x, y)…

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Q: Find √ √ (4x + 5y)dA where D = {(x, y) | x² + y² ≤ 9, x ≥ 0}

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Q: If y = ln(x√x² + 1), then A) 1 + X x² +1 B) 1 + dy dx 1 x√x² +1 C) 2x² +1 x√x² +1 D) 2x² +1 x(x² +1)…

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Q: 5. Let y = √5r²+2+7, determine from first principles dy

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