Use x as the midpoint of each subinterval to find the area under the graph f(x) = 4 – x² and the interval [-2, 2].

Q: Find the area under the graph of the function f (x) = xe-* between x 0 and x = 5.

A:

Q: Find the area bounded by the curve y and its asymptote/s. (1+x2)

A:

Q: Approximate the area under the graph of f(x) = x' over [1,3] by using N = 4 with left endpoints. 20…

A: The objective is to estimate the area under the graph of fx=x3 over the interval 1,3 by using N=4.…

Q: Find the area under the graph of y = -x² AL 54 3-2 -11° 1 2 3 4 5 X 4x on the interval [-4, -2].

A: We will solve the required.

Q: i. Find the exact area between f(x) 7x + 10, the x-axis, x 0, and x = 5.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: .Find the area under the graph of y = g(x) from -3 to 6, where x², g(x) = 18 – x, x > 2

A:

Q: Find the area under the graph of f(x)= x2 and above the x-axis, between x = 0 and x = 3.

A: Given, f(x) = x2, we have to find the area under the graph f(x) and above x-axis between x = 0 and x…

Q: c) Estimate the area under the graph of f(x) = sin x from x = 0 to x = using four approximating…

A: Given function is fx = sinx x∈0,  π2 number of rectangles = 4 Step size  h= π2 -04   = π8 ⇒ h = π8…

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 under the curve y = f(x) over the stated interval.

A:

Q: (a) Estimate the area under the graph of f(x) = 25 – x from x = 0 to x = 5 using five approximating…

A: Consider the equation as shown below: Here, the function fx =25-x2 And the object is to find the…

Q: Find the area under the graph of y = x² + l over the interval [-1, 2]. In this case, f(x) = x² + 1,…

A: area of graph within limits given by integrating function within limits

Q: Find the area of the region under the graph of the function f on the interval [4, 11]. f(x) = 2x - 2…

A: use integral to evaluate the are bounded by curve over the interval

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

A: Given curves

Q: Find the area under the curve y = 3x 2 from = 1 to x = 2 .

A: We have to find the area of the given curve.

Q: Let f(x)=3x°. /16 – x* - The area between the graph of f and the x-axis, on the interval [0,2] is..

A:

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: Q1. Use r; as the right endpoint of each subinterval to find the area under the graph of f(x) = 9 -…

A:

Q: Find the area of the region under the graph of f(x) = e−x/3 from x = 12 to x = 27.

A:

Q: Find the area of the region bounded by the graph of ​f(x)=sin x and the​ x-axis on the…

A:

Q: c). Find the area under the curve f(x) = 4x +2x over the interval (5,8)

A: Given,            fx=4x3+2x , the interval is 5,8To find : Find the area under the curve over the…

Q: Find the area under the curve y =3x2-2x from x= 1 to x =5.

A:

Q: Find the area enclosed between f(x )= 0.8x^2 + 9 and g(x) = x from x = −2 to x = 4

A:

Q: Use definition to find the area under the graph of f(x) = x² + x and above the x-axis on the…

A:

Q: Consider the area under the graph of f (x)=x – 3x, from x = 2 to x= 4. a. Estimate the area under…

A:

Q: Find the area under the graph of f over the interval [1,7]. 6x +5, for xs6 f(x) = 59-3x, for x>6

A: Given

Q: Use the form of definition of the integral with x as the right endpoint of each subinterval to find…

A:

Q: Compute the area between the following curves y = x° and y = -3x2 on the interval |0, 2|

A:

Q: Use Xk* as the right endpoint of each subinterval to find the area under the graph f(x)= 9-x2 over…

A:

Q: Find the area, if it exists, of the region under the curve on the given interval of the x-axis. f(x)…

A: Given. Y = e-3x Area is  dA = e-3xdx Interval is  X>=8

Q: Draw the graphs and find the area between the curves f (x) = x - x+3 and g(x) = -4x+1.

A: Let's find.

Q: Find the area under the curve between x-2 and x=-1 for the curve f(x)=(7 – x²)d

A:

Q: Find the area enclosed between f(x)=0.5x2+8 and g(x)=x from x=-2 to x=2.

A:

Q: Find the area under the curve f(x)=6 , bounded by the x-axis,x=1 and x=3

A:

Q: Let f (x) = 8/x^2  . Compute the area A of the region between the graph of f and the x axis on the…

A: Given: f(x)=8x2interval[−7,−4]

Q: Find the area under the curve y=x3+3x2 and the x-axis between x=1 and x3D3. O 46 sq. units O 54 sq.…

A: We need to find the area under the curve y=x3+3x2 on interval 1, 3.

Q: (b) Use the midpoint approximation M4 to approximate the area under f(x) = 3x – 2 on [1, 5). Show…

A: a. midpoint approximation

Q: Find the area under the curve f (t) = 3 − x2 + 5x from x = −2 to x = 4 .

A: Find the area under the curve f (t) = 3 − x2 + 5x from x = −2 to x = 4 .

Q: Find the area under the curve y = a²xe¬b²x from x = 0 to x = 5.

A:

Q: Use r as the right endpoint of each subinterval to find the area under the graph of f(x) = 9 – x²…

A:

Q: Find the area bounded by f(x) = -x² +4x +1 and g(x) =x+1

A:

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: b) Find the area enclosed between f(x)= = -x² + 4x and g(x) = x² - 6x + 5, over the interval 0≤x≤ 1.

A: Sol

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 between the curve f(x) = √x and g(x) = x³.

A:

Q: Approximate the area under the curve of y = x - 2x + 3 over the interval x=-1 to x = 3 using 4 right…

A: Find out the area under the curve using 4 right endpoint rectangles.

Q: - Use the midpoint sum formula to calculate the area under the curve f(x) = x³ from x=0 to x-12…

A: Here h = b-an = 12-04 = 3

Q: Find the area, if it exists, of the region under the curve on the given interval of the x-axis. 1…

A:

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.