Set up the definite integral that gives the area of the shaded region bounded by the graphs of y, =x² +2x+1 and y, = 2x +5 as shown in the figure to the right. (A) $(*+4x +6)dy -2 -1 1 2 3 (C) (x² +4x+6)dx (D) [(-x² +4)dy

Q: 8. For the enclosed regions bounded by y = x² - 6x and y = -2x in the graph, what is the integral…

A: Given   From the graph intersection point

Q: Find the area of the region bounded by y = -x² – 6x – 3, y= -x2 – 8x – 13, x = -5, x = -2.

A:

Q: Set up the definite integral required to find the area of the region between the graph of y=x2-17…

A: First draw the curves and find their intersection  points then use integration to get the area.

Q: Set up the integral of the area of the region bounded by the curves x=-y2+2 and x=y2-2

A:

Q: The integral of x^7(2x^6 - x^8) dx with limits -5 to 5

A: Evaluating the definite integral

Q: Set up an integral representation for the area of the region bounded by y=-x^2  and  y=-x-2

A: Given y=-x2 and y=-x-2

Q: Set up an integral representation of the area of the region bounded by: y=x3 and y=4x in the first…

A:

Q: Find the definite integral that will compute for the area of the region bounded by x = √y, y = 4-x²,…

A:

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

Q: Set up the definite integral that gives the area of the region bounded by the graph of y,-x+2x+1 and…

A:

Q: Compute the area bounded by the curve x=y²-2y and the line x-y-4-0₁

A:

Q: Find the area of the region that lies under the curve y = 4x-x over the interval 0<x<4. y = 4x - x

A:

Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: 4. Find the area of the region bounded by y = cos x, y = sin x, x = 0, x = %3| might have to break…

A:

Q: The area of the region bounded above by yx+7. bounded below by vey2, bounded from the left by x2 and…

A: The given region is as shown. Now, It is bounded above by y=x+7 and below by y=x2. So, the upper…

Q: The definite integral that calculates the area of the region enclosed by the curves y=4 - x² and y =…

A: Solution of the problem as follows

Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

A:

Q: 3) Find the area bounded by the curves: x² – 4x + 1 = 3y and x2 + 2x + 2y – 5 = 0.

A:

Q: Find the exact area of the region bounded by y = -x² + 3x +1 and y = -x+1

A:

Q: Determine the exact area of the region bound by the graph of f(x) = −x^2 + 5 and the x-axis on…

A:

Q: 2. Find the area bounded by y = ÷x' 3x and y = -4. - %3D 3,

A:

Q: A region is bounded between x = 0, y = 1, x = 1, and y = (x-1)^2+1. What is the area of this region?

A:

Q: Set up the definite integral required to find the area of the region between the graph of y = 12-2²…

A: we have to find out area

Q: Identify the definite integral that represents the area of the region bounded by the graphs of y= x…

A:

Q: The area of the region bounded by the curves y =x and y = 20–x² is попe 4.4 O 4= " |20–x²-x| dr -4.4…

A:

Q: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the area of the region bounded by y = 5-x2, y 2x+2, y=-x-1, a. in terms of x b. in terms of y y…

A: We will find out the required value.

Q: Find the area of the region that is completely bounded by the two curves f(x) = x* g(x) = 3x + 20. -…

A:

Q: Can i get help step by step?

A: We graph y=7x using a graphing calculator  The graph cuts  x-axis at x=0  So over the interval…

Q: 1. Find the area of the region bounded from the right by the curve x = 4 - y2 , from the left by the…

A:

Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area of 3. find the…

A: Given integral is ∫-42f(x)+2x+5dx As the region has been divided into three parts, A,B and C, so we…

Q: 2. Find the area of the region bounded by the graphs of y = x2 – 6 and y – 3 = 0. - -

A: Graphically: Now, the area can be found as the following.…

Q: How do I solve this problem?

A:

Q: 6. Find the area of the region bounded by the two curves of equat rens a) x=3-y² and f(x)= 3x (スー2)-…

A: Note:- In Part (a), you mention f(x) for 2nd curve but it is not mentioned for first curve. If i…

Q: 6. Sketch the region bounded by the graphs of y = 2 – x², and : and find the area of this region by…

A: For the Cartesian curves y1=f1(x) and y2=f2(x) where y2&gt;y1 in the limits x=a to x=b, the area…

Q: 2 Set up the definite integral required to find the area of the region between the graph of y = 20 –…

A:

Q: 6. Find the area bounded by the curves of y = 6x + x² andy = -x² - 2x, and the linex = 5.

A: The equation of the curves are  C1: y = 6x+x2C2: y = -x2-2xC3: x = 5 To evaluate: The area of the…

Q: Find the area under the curve 4x2-3x+6 between x= -2 and x=3

A:

Q: Consider the region bounded by F(x)=10x3 +7x2 -7x +6 and g(x)= 9x3 +8x2 - x +6. Find the area, in…

A: Given query is to find the area bounded by the curves for the given intererval.

Q: Find the area of the region bounded by y=-x^2+3x+1 and y=-x+1

A: Please see the diagram below to understand what's going on:

Q: Find the area of the region bounded by the curves y= x2 x3−3x and y= 1 x3−3x on the interval…

A:

Q: Find the area of the region bounded by y = (1/8)(-x2 + 6x + 7) and y = -6.

A: Solved below

Q: Set up integrals to find the area of the region between f(x) = (x-4)5 and g(x) = x-4. (integrals…

A:

Q: Set up an integral representation of the area of the region bounded by: y= 1/4x2 + 1/2x and…

A:

Q: Set up the definite integral required to find the area of the region between the graph of y = 20 –-…

A:

Q: a of the region bounded by y=4x-x^2 and y=x

A: the area bounded by two curves f(x) and g(x) is given by ∫abf(x)-g(x)dx now  y=4x-x2 and y=x2-2x…

Q: 1. Find the area of the region bounded by y = x² - 3 and y = 5 - x².

A: This question can be solved using the concept of area bounded by two curves.

Q: 2. Find the area of the region bounded by f(x) = 3x³ - x² - 10x and g(x) = 2x – x². %3D

A:

Q: Identify the definite integral that represents the area of the region bounded by the graphs of y = x…

A: We have to find the definite integral that represents the area of the region bounded by the graphs…

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.