Calculate the area, in square units, bounded above by g(x)=9x+9 and below by f(x)=10x−10 over the interval [−33,5]. Do not include any units in your answer

Q: Determine the area, in square units, of the region bounded above by g(x)=−8x+3 and below by…

A: Given g(x)=−8x+3 and f(x)=−7x+16 And the curve g(x) is bounded above and f(x)=−7x+16 is bounded…

Q: Evaluate the integral. 4 f(x) : 16 – x2 if -4 < x < 0 0 < x < 4 f(x) dx where if

A:

Q: Calculate the area, in square units, bounded above by f(x)=x2+4x+4 and g(x)=−4x+4 and bounded below…

A: Consider the curves, fx=x2+4x+4,   gx=-4x+4 To sketch the graph: Here there are two region be…

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [-1, 2] by…

A: Clearly the given integral can be approximated by the areas of the given triangles.

Q: Find the area, in square units, bounded above by g(x)=6x−1 and below by f(x)=7x−15 over the interval…

A: It is given that region is

Q: Find the area under the curve y = x3 + 3x2 and the x-axis between x = 1, and x = 3

A: Find the area under the curve y = x3 + 3x2 and the x-axis between x = 1, and x = 3.

Q: Determine the area to the left of g(y) = 3-y2 and to the right of x = -1

A: Area

Q: Use any method to evaluate the integral. dx X>11 (x²-121) 3/2

A:

Q: What is the total area between f(x)=−6x and the x-axis over the interval [−4,2]

A: Graph of f(x)=-6x in interval -4 to 2 is shown on board

Q: ind the area, in square units, bounded above by f(x)=x^2+10x+25 and g(x)=3x+33 and bounded below by…

A:

Q: Determine the area, in square units, of the region bounded above by g(x)=8x+6 and below by…

A: We have to find area between two curves in the interval [-10.15],for more clarification see graph.As…

Q: Determine the area, in square units, of the region bounded by f(x)=−4x−17 and g(x)=−5x+1 over the…

A:

Q: Find the total area between the curve of the function f(z) = -4z +8 and the z-axis over the interval…

A: I have provided solution in  step2.

Q: 2) Calculate the area, in square units, bounded by f(x)=10x³ +8x² −17x-4 and g(x)=9x³ +10x² - 2x-4…

A:

Q: Consider the region bounded above by f(x)=7x2+3x−45 and below by g(x)=8x2+22x+45. Find the area, in…

A: First, we need to find the points of interesection of f(x)=7x2+3x−45 and g(x)=8x2+22x+45At points of…

Q: Determine the area, in square units, of the region bounded by g(x)=−7x−7 and f(x)=x2 −11x−28 over…

A: To calculate the area bounded between the curve g(x)=-7x-7 and f(x)=x2-11x-28 over the interval…

Q: Calculate the area, in square units, bounded above by g(x)=2x+4 and below by f(x)=3x+9 over the…

A: Area of region between g(x) and f(x) over the interval [-26,-23] is computed as follows.

Q: b) Find the area between the 2 curves f(x)=x²+4-4x and x-axes and border with the two lines = 5 &x=…

A:

Q: Consider the region bounded above by f(x)=7x2+3x−45 and below by g(x)=8x2+22x+45. Find the area, in…

A: The given functions are,

Q: For the area under the curve f(x) = x(x+1)(x+7) above the x-axis, and between the vertical lines…

A:

Q: The area of the region between the x-axis and the carve y = e¯ -3x for x >0 is

A: Formula:For y=fx; y≥0 area between the curve y=fx, x=a,x=b and x-axisA=∫ba fxdxGiven y=e-3x

Q: Calculate the area in square units, bounded above by g(x)=4x+10 and below by f(x)=x2+6x−14 over the…

A: The given function g(x) and f(x) are line and a parabola over the interval [-6, 4].Since the line…

Q: Consider the region bounded above by f(x)=−2x3−9x2−10 and below by g(x)=−x3−12x2−10. Find the area,…

A: To calculate the area contained between the two given curves (as boundaries)

Q: The area under the curve y = Vĩ bounded from below by the 16 x-axis and on the right by x = 4 is…

A: Integration can be used to find area of region bounded by a set of functions. For two functions…

Q: Find the total area between f(x)=3x2-3 and the x-axis on the interval [-2,2]

A: Calculation:The given curve are f(x) = 3x2 – 3 and the x axis y = 0 on the interval [– 2, 2].The…

Q: Find the Area below f(x) = -x² + 4x and above g(x) = x² – 6x +5 over the interval 1 siS4. 3

A: Given    fx = -x2+4x   gx = x2-6x+5Find out area in interval 1≤x≤4Area = ∫14fx-gxdx          =…

Q: Determine the area, in square units, of the region bounded above by f(x) = -x² + 20x – 70 and below…

A: Given:  fx=-x2+20x-70 gx=x+20 To find: Find the area over the interval 9, 10. Required formula:…

Q: Calculate the area, in square units, bounded by f(x)=−5x3+3x2−8x−8 and g(x)=−4x3−4x2+2x−8 over the…

A: Given:  f(x)=-5x3+3x2-8x-8 g(x)=-4x3-4x2+2x-8 The interval is  3, 7. To find: We have to find the…

Q: Determine the area, in square units, bounded above by f(x)=−x2−10x−16 and g(x)=2x+16 and bounded…

A: Given: fx=-x2-10x-16gx=2x+16 We need to find the area bounded above by fx and gx and bounded below…

Q: 5) Calculate the area in square units, bounded by g(x)= 4x+8_and_f(x)=x² +19x+62 over the interval…

A: NOTE: Refresh your page if you can't see any equations. . here we have  and the interval is  so…

Q: Evaluate the integral. r5 x3 – 3x² – 9 dx J4 x3 – 3x²

A:

Q: Determine the area, in square units, bounded above by f(x)=−x^2−10x−16 and g(x)=2x+16 and bounded…

A: Given that fx=-x2-10x-16gx=2x + 16 The objective is to find the area of the region which is bounded…

Q: Find the total area between the curve of the function f(x)=2x+4 and the x-axis over the interval…

A: We have to find the total area under f(x)=2x+4 and the x-axis over the interval [−9,−1]Recall that…

Q: Calculate the area, in square units, bounded above by g(x)=8x−8 and below by f(x)=9x−12 over the…

A: Area of region between g(x) and f(x) is computed as follows.

Q: Calculate the area, in square units, bounded by f(x)=6x3−7x2−12x+9 and g(x)=7x3−24x2+58x+9 over the…

A: Given that, f(x)=6x3 −7x2 −12x + 9 and g(x)=7x3 −24x2 +58x + 9 To Determine area under the two…

Q: 1. Determine the area of f (x) = 3 + 2x – x² and above the x axis. - X - 3x 3 3 2. Determine the…

A: To find the area of f(x) and above the x-axis, use the formula, A=∫-13f(x)dx and substitute f(x)…

Q: Find the area of the region in the xy-plane bounded above by the graph of the function…

A: Given  fx=711x-2111, x=3 &amp; x=14 To find Area:

Q: The area between z = −2.27 and z = 1.41 is .

A: P(-2.27&lt;z&lt;1.41)=?

Q: Find the area bounded by the function f(x) equals .3x^3-1.5x^2+19 the X axis and the lines X=2 and…

A: We will find out the area under the curve.

Q: find the area between f(x)=x^2-16 and the x axis from x=0 to x-=9

A: The given function is fx=x2-16 We have to find the area between fx and the x-axis from x=0 to x=9

Q: Find the area of the region bounded by f(x)=X^2-4X +3 the X axis in the lines X=2 and x=6

A: We will find out the area of the region.

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [– 1, 2] by…

A: Given the graph of the function :

Q: nits, of the region bounded above by f(x)=9x+5 and below by g(x)=8x−7 over the interval [7,32]. Do…

A:

Q: 3 x° +x* dx x² 4 3

A: The given integral is solved below in detail.

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – 2° over the interval [0, 3] by…

A: Given function is f(x)=9-x2 we have to find the area over interval [0, 3]. Since there is 3…

Q: Evaluate the integral. [4 f(x) = | 16 – x² if 0 < x < 4 if -4 sxs 0 f(x) dx where

A:

Q: Find the area, in square units, bounded by f(x)=8x+15 and g(x)=7x+6 over the interval [−7,10]. Do…

A: The given functions are f(x) = 8x+15 and g(x) = 7x+6 over the interval [–7,10].

Q: – 30 - Evaluate the integral: -d.x x2 Vx2 + 16

A:

Q: find the area between y=2x2+9x-5 and y=-X2+6x+1 for x in (-2,2)

A: The given curves are,

Q: Find the area between  F(x) = x^2-5 and the x-axis from x=0 and x=9

A: Given query is to find the area under the curve.

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.