(b) Divide the interval [-1, 1] into 2n parts. Approximate the area under the curve by rectangles, using... i. .the left endpoint on subintervals of [-1,0] and the right endpoint on subin- tervals of [0, 1].

Q: Approximate the region under the curve f(x) = 2x + 1 by using the Riemann sum with 3 intervals using…

A: Width of each interval= (21-3)/3=18/3=6 so the partition is 3,9,15,21 For left Riemann sum we take…

Q: Consider the function f(x) = 4x2 −x3. Provide the graph of the region bounded by f(x) and the x-axis…

A: The solution is given below in the next step:

Q: Consider the region bounded above by f(x)=−x2+9x+7 and below by g(x)=8x+5. Find the area, in square…

A:

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

A:

Q: Find the area of the region bounded by f (x) = a /20 – 3x – 2x² and the x -axis using Right Riemann…

A:

Q: Find the area under the curve y Т over the interval [1,4]

A: Topic = Area

Q: 10. Find the area between y = 3x²+14 and y = 4x + 2 over the interval [-2 , 2]

A:

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 under the curve y = over the interval [1, 3 -

A: Given y=3xwe can use integration to find area under the curveArea=∫133xdx

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

A:

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

A:

Q: Use riemann Sum obtained by dividing the interval equal [4,3] into subinter vals to compute the…

A:

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

A: The given two curves that bounds a region is,

Q: The area bounded by the small loop of the line limaçon r= 1-2sintheta is given by the definite…

A:

Q: use the limit of the Riemann Sum to find exacct area under the curve. fCx) = 4 x [2,5]

A:

Q: Find the area of the region bounded by f (x) = a v 20 – 3x- 2x2 and the x -axis using Trapezoidal…

A: Trapezoidal formula can be simplified for calculation efficiency by factoring {\displaystyle \Delta…

Q: Find the area between the furve f(x) =sinx and g(x) = cosx over the interval [90. 360] y=4x+16 x=--2…

A: Dear as per company guidelines we can answer only one question at a time, kindly post other question…

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: What is the total area between f(x)=2x−7 and the x-axis over the interval [0,5]?

A:

Q: Estimate the area under the graph of f(x) = Vx + 1 over the interval [– 1, 15] using eight…

A: (1) To find the area under the graph fx=x+1 over the interval -1,15 using midpoint formula where…

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

A:

Q: Find the area of the region bounded by thegraph of ƒ and the x-axis on the given interval.ƒ(x) = sin…

A: Solution -  Given function is - f(x) = sinxWe have to calculate the area enclosed by f(x) from x =…

Q: 1 Estimate the area under the graph of f(x) over the interval [1, 5 using four %3D x + 4…

A:

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

A:

Q: Use a Riemann sum to approximate the area under the graph of f(x) = 2x2 on the interval - 2 SXs2…

A:

Q: Use a trapezoid sume with n=1 to estimate the area of the region trapped between f (x) = sin x +1 on…

A: Given,         f(x)=sinx+1;          0, π2

Q: Find the area of the region bounded by thegraph of ƒ and the x-axis on the given interval.ƒ(x) = cos…

A: fx=cosx, π2, π The diagrammatic representation of the area is,

Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

Q: Find the area under the curve 3 over the interval [3, 8]. y = (4x + 2)² Enter the exact answer. area…

A: y = 34x+22,interval : 3, 8

Q: Use a Riemann sum to approximate the area under the graph of f(x)=2e−x on the interval 1≤x≤2 using…

A:

Q: Estimate the area of the region bounded bythe graph of ƒ(x) = x2 + 2 and the x-axis on [0, 2] in the…

A: To Estimate: The area of the region bounded by fx=x2+2 and the x-axis on 0,2using Right Riemann sum…

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

A:

Q: Find the area of the region bounded by f(x) = -x² – 2x + 3, x-axis, and interval [0, 2].

A:

Q: Use the Riemann Sum to find the area for the region bounded by the graph of f(x)= 2x+3x^2 and the…

A:

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

A:

Q: Use a finite sum to estimate the area under the curve using the midpoint rule f(x)=x^3 on the…

A: Width of the interval [0,2] is = 2-0=2So for two rectangles the width of the subintervals=∆x=22=1So…

Q: Estimate the area under the graph of f(x) = 2x + 16x + 35 over the interval (0, 4] using ten…

A:

Q: Estimate the area under the graph of f(x) = x² – 2x + 5 over the interval (0, 7 using ten…

A:

Q: The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the…

A:

Q: The area bounded by the curves: у-х, у-6-х аnd у-0.5х is:

A: see below the answer and explanation

Q: To estimate the area under the graph on the interval [-4, 4], we use left-rectangle approximation…

A: Introduction: A sub-interval can be divided into a certain number of subintervals with equal length.…

Q: Find

A:

Q: Estimate the area of the region bound by the graph of f(x) = x^2 + 3x and the x-axis on [2,5] using…

A: The solution is given below

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

A:

Q: Estimate the area under the curve given by the function f(x)= ^3√x on the interval [1, 8] using 6…

A: The solution are next step

Q: What is the total area between f(x)=−2x−6 and the x-axis over the interval [−8,4]?

A: The area under a curve is the area between a curve f(x) and  the x -axis is the interval [a,b] given…

Q: Divide the interval (-1, 1] into four subinterval of equal length and compute the left-endpoints…

A:

Q: Find the approximation of the area under the curve using 4 trapezoids. Use the function y = x2 - 4x…

A:

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

A: Given :  Function f(x) = √(x+3), Interval [-3,1], To find : Area under the graph of given function…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.