3) Find the area of the region enclosed by the following curves. y = x² and y = -x² + 8x + 10 %3D

Q: 9. y = x²; y = 8-x²; y = 4x +12 %3D

A:

Q: Find the area bounded by the following curves and lines: 4y = x^2 - 2ln(x), y=0, x=1, and x=4

A: SOLUTION-

Q: nd the area of the region enclosed by the curves x = 5y, x 0, and y = 1.

A:

Q: 2 ア=x,y=2r

A:

Q: 3. Find the area of the region in the first quadrant that is bounded by y=Vx , x-axis and y=x-2. |

A: 3) To find the area under the curve in first Quadrant

Q: y=x² And y=-x+4¢

A: Given: y=x2   and y=-x2+4x

Q: 3) Find the area of the region enclosed by the following curves. y = -x? + 4x + 14 and y = (x - 2)2

A: As per the guidelines, only one question can be answered. I request you to kindly repost other…

Q: 1. Find the area of the region enclosed by the equations below. y = x² – 2x and y = x

A: Given function :

Q: 4. Find the area of the region bounded by the horizontal strip. y² +1 and the y-axis using

A: Topic = Area

Q: 3) Find the area of the region enclosed by the curves: y =x, and y = 2x – x

A: For the given curves  y = x2 and y = 2x-x2  Area of the region enclosed by the above curves are…

Q: Find the area of the region enclosed by r = y² and y = x – 2.

A:

Q: 6.(. Find the area of the region enclosed by the curves y = x² +1 and y = x +3.

A: I am solving this in step 2

Q: Find the area of the region enclosed by the graphs of 1 0, and x = 10 1 y = 0, x 1 — 25л2 NOTE:…

A:

Q: 10. Find the area of the region bounded by y = =.y = 1, and r = 3.

A:

Q: By sketching the graphs, find the area of the region bounded by, x = /y,y x + 6 and x = 0

A:

Q: Find the area of the region enclosed by x = y^2 + 2 and x = 2y+6

A: Please refer to the image below.

Q: Find the area of the region R enclosed by the parabola y = x2 and the line y = x + 2.

A: Given that y=x2          ...(1)y=x+2       ...(2)

Q: Sketch the region enclosed by the given curves and calculate its area. y= square root of x, y=0, x=4

A: Given,

Q: Find the aea of the region bounded by 2. given Curves

A: We have to find the area bounded by the given curves. This problem can be solved by using…

Q: 6. Find the area of the region enclosed by the graphs of y = VT+1 and y = r – 2 and the vertical…

A:

Q: 5. Calculate the area of the region enclosed by the graphs of y = 2r- r and y = 0.

A: We first find where they meet Plug y=0 in y=2x-x2 and solve for x

Q: Find the area of the region enclosed by the graphs of the given equations by partitioning the…

A: Given: y=x, y=x3, about x-axis

Q: Find the area of the region enclosed by the graphs of 1 VI- 472' Y =0, x = 0, and x = 4' 1 — 4г?

A:

Q: (b) Find the area of the region enclosed by x = y² and y = x – 2

A:

Q: Find the area of the region bounded by the following curves, showing all workings: x=1, x 4, y =x² -…

A: For the cartesian curves y1=f1(x) and y2=f2(x) where y2>y1 in the limit x=a to x=b, the area…

Q: 4. Find the area of the region enclosed by y = –x² + 6, y = x, y = 5x, and x 0.

A: Area bounded by the region y=-x2+6, y=x and y=5xFirst we sketch the region

Q: Find the area of the region enclosed by x = y and x = Vy– 6.

A: The graph is shown below:

Q: Find the area of the region enclosed by the curves y = x + 5, y² = = x, y = −1, and y = 2.

A:

Q: (1) Find the area of the region bounded by the curves and draw an illustration y = x² and y = 6x-x².

A: The region bounded by the curves y=x2 and y=6x-x2 Note:    Multiple questions are given we are…

Q: Calculate the area of the region that lies under thecurve and above the  x-axis. y =1- x2

A: The graphical representation of the area is,

Q: Find the area of the region enclosed by the graphs of 1 1 y = %3D V1– 972' 9 = 0, x = 0, and r 6. |

A:

Q: 10. y = x; y = x'; x+ y = 2

A: Function is the unique relation, where each x is mapped to unique y. It can be of many type,…

Q: Find the area of the region enclosed by the graphs of 1 1 1 – 16æ²' Y = 0, x = 0, and æ NOTE: Enter…

A:

Q: 3. Find the area of the region enclosed by the two curves y = x² and y = -2x² + 3x.

A:

Q: 3. Find the area of the region enclosed by the given curves. y = Vx + 2, 1 y = x = 0, x = 2 %3| x…

A: Recall: If f(x) and g(x) are two continuous function and f(x) ≥g(x) on the closed interval [a,b] ,…

Q: Find the area of the region bounded by the given y = 4ax, y = 4ax°, a > 0

A: The given curves are  y = 4ax y = 4ax3 Intersection point of both curves 4ax = 4ax3 4ax(x2 - 1) = 0…

Q: Find the area of the region enclosed by the given curves. y = 13-x2, y=x2-5

A:

Q: What is the area of the region bounded by the graphs of y = x³ – 2x² + 1, x = 1, x = 3 and the…

A:

Q: y² = x y = x³

A:

Q: Find the area of the region enclosed by the following curves : y2 = x+2 and y = x.

A: We have to find the area of the region enclosed by the given curves   Given curves are y2 = x+2…

Q: 2. Find the area of the region enclosed by the curves and x, 0 < *< 2. y = y = (x2 + 1)2 4*

A:

Q: 2. Determine the area of the region bounded by x = y? – 4 and y = and sketch a graph of the region.

A: We graph the region using a graphing calculator  y=x/3 (red) x=y2-4 (black)

Q: Determine the area of the region between the x-axis and the graph of the curv -1 from x- 0 to x- 4.…

A: Area bounded by curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on a,b…

Q: Find the area of the region described in the following The region bounded by y = 24 Vx and y = 3x?

A: Given, y=24x &amp; y=3x2 To find limits of x we have, y=24x =3x2⇒24x =3x2⇒8x=x2 Now squaring on the…

Q: Find the area of the region enclosed by the graphs of x + (y – 1)² = 1 and 2x = -y?.

A:

Q: 2. Find the area of the region bounded by y = VI and y = r.

A:

Q: = 2. Find the area of the region enclosed by the curves Vx and y = x² between x = 1 and x =

A: Given curves x2 and √x To find the area of the region enclosed by the curves between x= 1 and x=2.

Q: 9) find the area of the region enclosed by: x= y' and x=-3y' +36

A: From the given problem: x=y2 : x=-3y2+36   So, the bounded region is shown below:     Finding the…

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.