Consider the function f (x) = –x² +9. What is the approximation of the net area under the curve of f using left-handed rectangles on the interval -12, –4] with four equal subintervals?

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A:

Q: Use the limit definition of definite integral in the form of f(æ) dæ = lim {(#:)Ax, i=1 6 - a and r;…

A:

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A: The function is given as fx=cos x The interval is given as 0, π2

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: Use the indicated method to approximate the area under the curve f(x)= x³ +28 on the interval [-3,…

A:

Q: Find the area under the curve f(x) = sin x bounded by x ∈ [0, 3]

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

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: Consider the function f(x) = x² - 3x + 2 on [0,4], Find the total area between the curve and the…

A:

Q: Let f be the function defined by S1+x, when 0<x<}, }<x<1 0, when x-1. f(x)= Show that fis integrable…

A: Recall the Result/Theorem A bounded function f which has only a finite number of points of…

Q: d) Use the right endpoint rule to approximate the area under the curve of f(x) = 4- x2 on [1,2]…

A:

Q: Approximate the area under the curve of y = x² - 2x + 3 over the interval x = -1 to x = 3 using 4…

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: What is the area under the curve of f(x) = 4 from r = 2 to r = 6? %3D

A: To find the area under the curve of f(x) = 4 from x = 2 to x = 6 Area = ∫26f(x)dx

Q: find the area between f(x)=x2 +16 and the x-axisn from x=0 to x=8

A: To determine the area between the curve and x-axis.

Q: Find the geometric area of the region bounded between the graphs of f (x), g(x) as given: f(x) = x2…

A: Sketch the graphs as shown below.

Q: Let f(x)=-2x^ 3 +6x^ 2 -x+1, Use L 4 to estimate the area under the curve or the interval [- 1, 1]…

A: L4 is the left endpoint of the expression with 4 approximating rectangles.

Q: Consider the function f (x) = -x² + 3x + 9. What is the overestimate of the area under the curve of…

A:

Q: 39. For the function f(x) = e + e, prove that the are length on any interval has the same value as…

A:

Q: In the given question , use the Midpoint Rule with n = 4 to approximate the area of the region…

A: Consider the provided function, fx=tanx, 0,4 Use the Midpoint Rule with n=4 to approximate the area…

Q: Express the limit as an integral. (7(x;)? - 2(x;)³Ax over [0, 4] lim i = 1 dx

A: This question can be solved using the limit definition of integration.

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

A: Please see the attached pic. The given line f(x) = 2x+3 has been plotted. The range [-4,2] is shown…

Q: Let f(x) = - 2x ^ 3 + 6x ^ 2 - x + 1 Use to estimate the area under the curve on L 1 the interval [-…

A: Using Riemann right end points sum, then limits

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A:

Q: Given f(x) = r +x+2, approximate the area under the curve for - 5 sxs3 using 4 left endpoint…

A:

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

A:

Q: The function fCx) is defined by an integral Vi+8sin't dt %3D Find an expresion for f'(x)

A:

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: What is the area under the curve of f(x) = 4r from r = 2 to r = 6? %3D

A:

Q: The function f(x)=4e^x is defined over the interval [-2,3]. Appproximate the area A by partitioning…

A:

Q: 1- Find integral result for f f e**+* dydx, where R the semicircular region bounded by the x-axis…

A: (1) We have to find the integral ∬Rex2+y2dydx, where R is the semicircle region bounded by the…

Q: Find the area of the region between two curves f(x) = 3x + 1 and g(x) = x from x = 0 to x = 1.

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

Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.

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: (Area Under a Curve)

A:

Q: Consider the function y (x) = 1 + ex / 2, from the point (0,2) to (4, e2). Set up the integral that…

A: Given that: y(x)=1+ex/2

Q: b) Compute the integral of the function using the trapezoidal rule, Simpson's 1/3 rule, and…

A: We'll answer one question, since the exact one wasn't specified. Please re submit the question which…

Q: Find the area A of the region between the graph of f and the x axis on [-1, 1].

A: Please see the white board for equation formulating the calculation of A.

Q: 8. Find the area under the curve of f(t) = 1.2e0.1t betweent=1 and t = 2. %3D

A: From the given statement, the function

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

A:

Q: Find the area under the curve f(x) = x° on x =[- 2.5, 5.5] using the Midpoint Rule with n = 8

A:

Q: Find the area bounded by the two curves f(x) = x2 – 8x + 8 and g(x) = - x² + 6x – 8, and the two…

A: The given two curves:fx=x2-8x+8 and gx=-x2+6x-8and the two vertical lines are x=3 and x=4.We need to…

Q: Consider the function f (x) = x² + x + 2. What is the maximum approximation of the area under the…

A:

Q: Let f(x) = x³+1, x<1 1 X+4 5 1.8976 x≥1 Use the composite Simpson's rule to approximate the integral…

A: Introduction: The formula for Simpson's 1/3rd rule is given by,…

Q: Consider the region bounded by f(x)=−x2+11x−3 and g(x)=5x+5. Find the area, in square units, between…

A: Given:

Q: f(x) X. 0.3 0.1 0.5 0.7 0.9 0.9 1.4 1.2 2.2 1.0 2.3 0.9 2.5 0.8 2.6 0.7

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.