1. Evaluate , 3y e ²x dA where D is the region bounded by x = ₁x = 1, y = 1 and y = 2. 2

Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…

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Q: . Find a number k > 0 such that the area of the region bounded by the curves y = x², and y =k – x2…

A: As per as our guide line I am supposed to answer only one question from these 2 question Please…

Q: Find the area of the region lying between the x-axis and the curve In(82) – 1 to the right of the…

A: Given curve is: y=ln8x-1x2 The area of region of the curve lying between x-axis and right of the…

Q: 3. Find the area of the region enclosed by y = 2 sin x, y = sin 2x, and 0 <x < T.

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Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given curves are y=x2-3x y=x3+x2-12x Take  y=fxHere,   fx=x2-3x y=gxHere,   gx= x3+x2-12x

Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

Q: The region between the lines y=2x, y=x/3 and x=3.

A: Detailed solution of the problem is given below. Explanation:Step 1: Step 2:

Q: 1.) Find the area of the region bounded by the parabola y = 2x and the line y = x - 4

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Q: II. Evaluate fS (x – y)dA where R is the region above the x -axis bounded by y2 = 3x R and y? = 4 –…

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Q: 3. Find the area of the region bounded by the curve y = Vx – 1, the y - axis and the lines y=1 and…

A: Simplify the equation y=x-1 to obtain the expression of x. y=x-1y2=x-1x=y2+1 Draw the graphs…

Q: 1. Find the Area of the shaded region. а. y (1/2)x2 + 2 y = -X -2 y = x3 - x2 - 6x 2. b.

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Q: 2. Find the area of the region between the curve, x = y² + y −6, y- axis and y=0; y = 3.

A: we need to find the area bounded by the given curves.