Consider the function f(x)=5sin(pi*x-pi/2) / (x2+4x+5) +5*1.1-(x+2), which is graphed the interval below on the interval [-2,8]. As a step in estimating the area under the curve from x= -2 to x=8, estimate the area under the curve from x=4 to x=8 using the trapezoid rule and 1 subdivisions. You get (from 4 to 8) Area= A. 2.283 B. 9.131 C. 9.383 D. 31.645 E. 4.565

Q: f(x) = 3x2 + 8x − 3  from  x = 1  to  x = 2

A: Given: f(x) = 3x2 + 8x − 3  from  x = 1  to  x = 2 Area=∫abf(x) dx That is, Area=∫123x2+8x-3 dx To…

Q: Approximate the area under the curve y=1x between x=1 and x=5 using the Trapezoidal Rule with n=4…

A: Width of each interval = (5-1)/4= 4/4=1 So the partitions are 1, 2, 3, 4, 5

Q: Approximate the area under the curve of y = -+x+5 over the interval x = -1 to x = 4 using 5…

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Q: Consider the function f (x) = –x² +9. What is the approximation of the net area under the curve of f…

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Q: Estimate the area under the graph of f(x)=f(x)=3x2+18x+29 over the interval [0,6] using five…

A: Given that, the function          f(x) = 3x2 +18x+29   and the interval  [0,6] Right endpoints…

Q: Estimate the area under the graph of f(x) = x² + 3x +1 over the interval [3, 5] using five…

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Q: Estimate the area under the graph of x) - 5 cos(x) from xO to xR/2 using four approximating…

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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 beneath the curve g(x) = 8x + 3x2 from x = 5 to x = 6

A: Given function is,

Q: Find the area under the curve y = - over the interval [4, 9]. (4x + 2)² Enter the exact answer. area…

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Q: Find the area between the curve f(x) =sinx and g(x) = cosx over the interval x=-2 and x=5

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

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Q: Consider the region bounded by g(x)=7x−6 and f(x)=x2+19x+14. Find the area, in square units, between…

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Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

A: Given curve: fx=x2+1 We have to find area under the given curve from x=0 to x=2. It is given that we…

Q: The sum that best approximates the area under the curve between the function and x-axis on the…

A: our objective is to find the best approximation

Q: Estimate the area under the curve f(x) = 2x from 0 to 1 using R4. Leave your final answer as exact…

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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: Approximate the area between f (x) = x² + 6x + 5 and the x -axis on the interval [0, 2] using 4…

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Q: 4. Find the approximate area under the curve f(x) = x³ – 3x² + 7 on the interval [0.97,3.4]. Use…

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Q: Approximate the area under the curve y=f(x)=1/x  on the interval [1,4] , Using 3 rectangles

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Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

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Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

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Q: Find the area between the curve f(x)=x^3−110 and the​ x-axis from x=1 to x=3.

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Q: Find the area between the curve y=2x+4x-6 and the x-axis from x =-2 to x= 3.

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Q: Approximate the area under the curve of y =-x+ 5 on the interval [0,2] using a right hand…

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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: Use a right-endpoint approximation to estimate the area under the curve f(x)=4x3+3 over the interval…

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Q: Find the area under the curve f(x) =x+3x+7, above the X axis from x=4 to x=6.

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Q: Find the area under the curve y = - - over the interval [4, 9]. (4x + 2)² Enter the exact answer.…

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Q: The area between the curve y = = and the x-axis from x = 10 to x = 20 is the same as the area…

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Q: Estimate the area under the curve of f (x) = x3 – 4x on [-1, 3] by calculating Lg and Rg. %3D

A:

Q: Find the area under the curve f(x) = 3x+ 1 over the interval [2, 6] with n = 4 by using right end…

A: Given f(x)=3x+1, a=2, b=6, and n=4.

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = 6e^x…

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Q: 1. Find the area under the curve y = 9- a2 over the interval[0, 3] using right end point…

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Q: 3) f(x) = 2x + 5, on the interval [–1,4]. Use RRAM and five sub-intervals to approximate the area…

A: Note:  According to the guidelines issued by the company we should answer only one question, please…

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 bounded by y2 = 4a(y - x), y2 = 2a(x + 2y – 3a) and the x-axis. Show complete solution…

A: To find the area:

Q: Find the area under the curve y 5 -over the interval [4, 7]. (3x + 1)² Enter the exact answer. area…

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

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Q: Find the total area between the function f(x)=3x+8 and the x-axis over the interval (−4,−1). Submit…

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Q: 3 Find the area under the curve y over the interval [3, 8] (4x + 2)?

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Q: Find the area under the graph of f(x)= sin' 2x cos 2x on the interval [0, 4).

A:

Q: Approximate the area under the graph of f(x) = 0.03x* - 1.44x + 43 over the interval [3,7] by…

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Q: Find the area under the curve y = over the interval [4, 7]. (4x + 3)2 Enter the exact answer. area =

A:

Q: Using the right-hand endpoint with n = 8 to write the Riemann Sum that describes the estimation of…

A: Given: n = 8 f(x) = x2 + 1

Q: Use the right endpoint sum to approximate the area under the curve f (x) = x^3 from x = 1 to x = 2…

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Q: Estimate the area under the graph of f(x) = 3 cos(x) from x 0 to x = 7/2 using four approximating…

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Q: Approximate the area under the curve f(x)=sin2(πx) using the midpoint approximation rule with 3…

A: Using a sum of midpoint rectangles calculated with the given formula

Q: Find the area bounded by the curve f(x) = x³ + 3x² – 4x – 5 and x-axis from x = -3 to x = -1 using:…

A: Consider the given area bounded by the curves as y=x3+3x2-4x-5 and the x axis from x=-3 to x=-1. Let…

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.