10. Approximate the area of the region bounded by the graphs of the equations given below using rectangles and 4 equal length sub-intervals, once with a "left" approximation and once with a "right" approximation (as indicated in "take- home" problem 1). Compute the average of the two approximations to improve your approximation of the area of the region. y=0, y=1+, x=-1, x=3 x2 3'

Q: 5. Find the equation of the line x = k that divides the area enclosed by the graphs of x = Vy,x = 3…

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Q: Determine the area between the graphs of the equations y=x and y=(x)^2-1. Integrate over the x-axis…

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Q: Consider the image attached of the graphs of y = (1/2)x + 5 (what the red line represents) and y =…

A: Given y=12x+5  and y=x

Q: Find the of the region bounded by the parabolas y – 6x = -x² and y + 2x = x² , area

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Q: 1) Find the area bounded by curve y = xvx2 + 1 and the lines x = 0, x = 4 an %3D the x-axis.

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Q: 15. Find the area between the curves x = y? - 4 and x = 8- 2y.

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Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

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Q: 1 1 from x=1 to x=3. 4x 3 5. Find the length of the curve given by y 3

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Q: Find the area of the region bounded by the curves x²y = 2, x²y = 3, y = x and y = 2x.

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Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: 2. Find the area of the region bounded by y = 2x² +10, y = 4x+16, x = -2, and x = 5.

A: first draw bounded region then find limit of region and using vertical strips find the area

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