Calculate the area under this function over the specified interval: f(x) = x² +2x – 1 ;[-4,5] Show all the steps of your calculations to obtain full marks. Area = Answer:

Q: Find the area of the region under the graph of the function f on the interval [1, 4], f(x) = 6Vx 32…

A: We have to find area under the graph.

Q: Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

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

Q: Find the area between the graph of function and the x-axis over the given interval, if possible.

A: fx=5x-22,  (-∞, 1].

Q: Find the area between f(x)=x²-7 and the x-axis from x = 0 and x = 6. ...

A:

Q: Find the net signed area between the graph of the function f(x) = |x +3| – 4 and the r-axis over the…

A: Given: f(x)=x+3-4 and the x-axis over the interval -9, 3 To find the net signed area between the…

Q: Find the area of the region under the graph of the function f on the interval [4, 5]. f(x) = 2…

A: The given function is fx=4x2 on the interval 4,5.

Q: Find the area enclosed by the curves f(x)=39-x2 and g(x)=x2

A: Given curves

Q: Find the area of the region under the graph of the function f on the interval [5, 11]. f(x) = 4x - 6…

A:

Q: What is the net signed area between f(x) = 2x + 3 and the x-axis over the interval -4,2]? Do not…

A: Given problem is : What is the net signed area between f(x)=2x+3 and the x-axis over the interval…

Q: Find the area enclosed between f(x) = 0.65x² + 7 and g(x) = x, on the interval from x = -3 to x = 5.

A: Given,  fx = 0.65x2+7 gx = x  We have to find the area enclosed between fx and gx on the interval…

Q: 2) Find the area of the function f(x)=x² +4 for x=-1 tox=4.

A:

Q: Estimate the area under the graph of f(x) = x² + 2x + over the interval (2, 4 using ten…

A: Rn = 34.28 Ln= 31.08

Q: Find the area of the region bounded by the graph of f and the x-axis on the given interval.…

A:

Q: Find the exact area between the graphs of f (x) = 2x +1 and g (x) = 9 – x2. First find out where the…

A:

Q: Approximate the area under the graph of F(x) = 0.7x° + 7x - 0.7x-7 over the interval [-7,-2] using 5…

A: Given, The area under the graph of f(x) using the left Riemann sum is given by where,

Q: find the area of the region under the graph of the function f on the interval [4,10]  f(x) = 8x - 5…

A: Area of trapezium

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: Approximate the area under the graph of F(x) = 0.7x +7x-0.7x-7 over the interval [-7,-2] using 5…

A:

Q: Estimate the area under the graph of f(x) = 36 – 2 over the interval [– 3, 4] using ten…

A: We need to find area using Reimann sum.

Q: Estimate the area under the graph of f(x) = x² + 3x + 1 over the interval [2, 4] using ten…

A: Given function: fx=x2+3x+1 Interval: [2, 4]Number of rectangles = 10 To find: The area under the…

Q: Find the area bounded above by the function f(x) = -3x² + 4x - 1 and bounded below by the x-axis.…

A:

Q: Find the area of the region under the graph of the function f on the interval [1, 4]. f(x) = 6Vx…

A: Given function is - f(x)=6x We need to find area of the region  under the graph of f(x) on interval…

Q: Find the area of the region under the graph of the function f on the interval [-27, -1]. f(x)=…

A:

Q: Answer with all details, find the area bounded between x-axis and function f(x) = x² – 2x with…

A: The graph is

Q: Find the area of the region under the graph of the function f on the interval [5, 9]. f(x)= 7/x2…

A:

Q: Estimate the area under the graph of f(x) = between x =1 and x = 7 using the midpoint rule" with two…

A: According to the mid-point rule, we divide the interval into n sub-intervals and consider the height…

Q: Find the area under the graph of y = g(x) from -3 to 6, where x², x 2

A:

Q: Estimate the area under the graph of f(x)=5/x from x=1 to x=7. Approximate using 6 rectangles.A.) If…

A: There are 6 rectangles  So each rectangle is of width = (7-1)/6=6/6=1 So, endpoints are…

Q: Find the area of the region under the graph of the function f on the interval [1, 5]. f(x) = 3x³…

A:

Q: f(x) = 3 + 2x2 from x = −1 to

A: Given: f(x)=3+2x2 from -1, 2

Q: Find the area, in square units, bounded by f(x)=3x+5 and g(x)=2x+1 over the interval [0,12]. Do not…

A: Area of region between f(x) and g(x) over the interval [0,12] is computed as follows.

Q: Find the area in the first quadrant bounded by f(x)=4x-x^2 and the x-axis.

A:

Q: Find the area of the region under the graph of the function f on the interval [1, 6]. f(x) : square…

A:

Q: a) Estimate the area under the graph of f(x)=2x+1 from x= 1 to x=2 using four approximating…

A: Given problems:- a).  Estimate the area  under the graph f(x) =2x+1 from x=1 to x=2 using four…

Q: Find the area of the region under the graph of the function f on the interval [1, 4]. f(x) = 5Vx…

A: The function is given by fx = 5x To evaluate : The area of the region under the graph of the…

Q: Find the area bounded by the curves f(x) =x and g(x) =x4

A:

Q: Estimate the area under the graph of f(x)=1x+3f(x)=1x+3 over the interval [1,3][1,3] using eight…

A: Given We need to find the area under f(x) over the interval [1,3].

Q: Find the area between the curves, f(x) = ;x² and g(x) : - x over the interval [0, 2] 10 3 - 1/3 2.

A: We first sketch the region

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: Calculate the area, in square units, bounded by g(x)=4x−2 and f(x)=5x−15 over the interval [−11,4].…

A: We need to find the area bounded between the curves g(x) = 4x-2 and f(x) = 5x-15 between x = -11 and…

Q: Find the area under the graph of f(x) = r² + 5 between x = 0 and = 6. %3D

A: The function is given by fx = x2+5 To evaluate: The area under the graph of the function fx between…

Q: Find the area under the graph of y = g(x) from -2 to 5, where x³, 4 – x, x 1 -

A:

Q: . Find the area between the curve f(x) = √x and g(x) = x³.

A:

Q: Find the area of the region under the graph of the function f on the interval [1, 9]. f(x) = 3/x…

A:

Q: Find the area under the graph of f over the interval [-2,4]. .2 X+6 XS2 f(x) = %3D 5x x> 2

A: To find the area under the graph of the function fx over the interval -2, 4.fx=x2+6,   x≤25x,…

Q: find the area of the region under the graph of the function f on the interval [-27,-1]  f(x) = 1 -…

A: Here Area under a curve on an interval is  analogous to the integral of the function of the curve on…

Q: Find the area of the function below over the interval, [0, 4].

A: Given graph of the function,

Q: Find the area bounded by the line f(x) = 3x - 5, the curve g(x) = x² – 10x + 7, and the two vertical…

A:

Q: Use R6 to determine the area under the curve for f(x) = (2-1) on [2,5].

A: Given that fx=1xx-1 To find : Area under curve of fx on 2,5Solution :

Q: Find the area enclosed by the curves f(x)=38−x^2 and g(x)=x^2.

A: Solving

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.