Sketch the region defined by the inequalities -1 ≤ r ≤ 2 and-π/2 ≤ u ≤ π/2.

Q: R is the region bounded by y = x² – 2x and y = x – 2.

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Q: Sketch the region bounded by the graphs of the functions. y = x3 - 6x, y = -2x² – 3x

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Q: Consider the region bounded by the graph of y = 4x + 3, the x-axis, and the lines x = 2, x = 7. A…

A: Given area bounded by the curve y=4x+3, x-axis and the lines x=2, x=7

Q: Sketch the region in the xy-plane defined by the inequalities x- 4y 0, 2- x - 7lyl 20 and find its…

A: Given region are   x-4y2≥0 and 2-x-7|y|≥0

Q: sketch the region defined by the inequality. 0 ≤ r ≤ 2 - 2 cos θ

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Q: Determine the region bounded x=y2-6y+10 and x=2y+4

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Q: What is the area of the region defined by the inequalities: y -2x – 1

A: This question can be solved using the concept of graph of inequation to obtained the shaded area and…

Q: Find the extreme values of f on the region described by the inequality. f(x, y) = 2x2 + 3y2 - 4x -…

A: we use langrange multiplier method

Q: The region R lies on the lines x – y = 8, x + 7y = 8, x - y =| and x + 7y =

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Q: Find the extreme values of f on the region described by the inequality. f{x, y) = e-Xy; x2 + 4y2 < 1

A: We will lagrange's multiplier here

Q: Sketch the region in the xy-plane defined by the inequalities x - 5y2 > 0, 2 – x – 9\y| > 0 and find…

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Q: Sketch the region defined by the inequalities 0 <r< 2 sec 0 and -T/4 < 0 < T/4.

A: The given inequalities are

Q: The region between the graphs of y = x² and y = 3x is rotated around the line x = 3.

A: Given data:   The expression first curve is: y=x2. The expression for the second curve is: y=3x. The…

Q: Find the number  b such that the line  y = b divides theregion bounded by the curves y = x 2  and y…

A: Given Data The equation of curve is y=x2. The equation of line is y=4. The equation of another line…

Q: Sketch the region given by the set. {(x,y) | x2 + y2 &gt; 4}

A: x, y  x2+y2&gt;4 It contains the region that lies outside the circle x2+y2=4.

Q: Find thearea bounded by x=y^2 and y=-x^2

A: The region is bounded by x=y2 and y=-x2

Q: Find the number k > 1 such that the region bounded by the curves y = 1, y = x-2, and x = k k has…

A: Given curves are y=1 and y=x-2 and interval is x=1 to x=k

Q: Use vertical strips to determine the region bounded x=y2-y-6 and x=2y+4.

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Q: Determine whether or not the region bounded by the curves is vertically simple and/or horizontally…

A: Given :               x = y2  ,  x = 2 - y2

Q: Sketch the region given by the set. {(x,y) | 0 ≤ y ≤ 2}

A: Consider the region given by the set {(x,y)|0≤y≤2} Observe that the given set includes all the point…

Q: Solve for the region bounded by y=9-x^2 and y=x^4.

A: To find- Region bounded by the given curves.

Q: Sketch the region defined by the inequalities 0&lt;= r&lt;=2 sec u and -pai/4 &lt;= u&lt;= pai/4

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Q: rotate the region bounded by y=2x+1, x=4 and y=3 about the line x=-4

A: Solution:-

Q: he region bounded by x2 + y2 = 4?, 4y = -5x and 13y = 6x where y 2 0. Leave your answer correct…

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Q: 5. Sketch the region in the -plane defined by the equation or inequalities a. -1&lt;=y&lt;=3 b.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Determine the region bounded x=y2-y-6 and x=2y+4

A: First of all we need to calculate meeting points.

Q: Find-the-approximate area-of-the-region-bounded-by-the-curves y = x/Vx2 + 1•-and-y x4 - x1 %3D

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Q: Provide inequalities that describe the region bounded by Z 3, y 0, y = 4-x, andz=0, as pictured…

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Q: Find the areas of the regions enclosed by the curves x + 4y2 = 4 and x + y4 = 1, for x ≥ 0

A: Solution:-  we have to find the are of the region bounded by the region bounded by the curve  a)…

Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Describe in words the region in R³ that satisfies 2x - z² ≤ x² + y² ≤ y² + 10

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the area of the region bounded by y = -4x + 9, y = 2x? – 11x + 9, and the lines x = -2 and x =…

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Q: Sketch the region in the xy-plane defined by the inequalities x- 5y 2 0, 2 - x - 9lyl 20 and find…

A: Graph of the curves÷

Q: Find the three areas of the region bounded by y= 2x2+10, y=4x+1 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+1x=-2x=5……1   To find: Area of the region enclosed with the above curve and…

Q: Determine the absolute maximum and minimum values of f(x, y) = 2+4x–2x²+4y-y² on the region R…

A: The region bounded by the x-axis,y=3x and x=2 is:

Q: Find the extreme values of f on the region described by the inequality. f(x, y) = x2 + y² + 6x – 6y,…

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Q: Sketch the region enclosed by the given curves. y = 14 - x2, y = x2 - 4 y y 15 5| 10 -6 -2 2 4 -10…

A: we have, y=14-x2,y=x2-4 region between two curves will be :

Q: Sketch the region given by the set. {(x,y) | x ≥ 2}

A: The given set is x, y | x≥2. Sketch the region of the above set as shown below.

Q: Evaluate where D is the region bounded by the semicircle x = /4– y² and the y-axis.

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Q: Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area of…

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Q: Sketch the region defined by the inequalities -1&lt;=r&lt;= 2 and -pai/2&lt;=u&lt;=pai&gt;2

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Q: Find the extreme values of f on the region described by the inequality. f(x, y) = 2x2 + 3y2 − 4x −…

A: Given: Th function is fx,y=2x2+3y2-4x-2 on the disk x2+y2≤16. Definition used: The Lagrange…

Q: Using your previous work, find the region bounded by the curves y = x² and y = x³.

A: Given that, There are two curves following, y = x2  and   y = x3 We have to find the area bounded by…

Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x – 10

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Q: R is the region bounded by y = -x² – 3x + 6 and x + y – 3 = 0 and it is revolved about x = -4.

A: Given that, R is the region bounded by y=-x2-3x+6 and x+y-3=0 and it is revolved about x=-4

Q: Sketch the region bounded by the graphs of the functions. y = x2 + 9x – 14, y = 9x - 5 y y y 40- 40…

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Q: Find the extreme values of f (x, y) = x² + y² + 4x – 4y inequality x² + y? < 9. on the region…

A: We are given that f(x, y) = x2 + y2 +4x-4y  We have to find extreme values of f(x, y)  On region…

Q: The region shown below is bounded by the curve y = 2x3 and the lines x = 8 and y = 3.

A: Given y=2x13 and lines x=8 and y=3. ax=y38when x=8⇒y=4 when y=3 ⇒x=278 By washer method,…

Q: Sketch the region in the xy  -plane defined by the equation or inequalities. |x|&lt;4 and |y|&lt;2

A: x&lt;4  and  y&lt;2⇒-4&lt;x&lt;4  and  -2&lt;y&lt;2   ∵x&lt;a⇒-a&lt;x&lt;a

Q: f the region bounded by the curves y = x3-8x2

A: The region bounded by the curves are y=x3-8x2+20x , y=-x2+8x…

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.