Question 1: Integrate function fo0 given below from x=4 to x=12 using the Trapezoid Method and find the Area under the curve of this function. Divide the interval [4,12) into n=4 equal subintervals. Calculate function values and the Area up to 4 decimal digits. Report the Area and f(a»), fla2), f(aɔ), flad). This notation refers to the one we used in our class notes shown in the table on the right. S(b) f(a,) f(a,) f(a,) 1 b 2 (b;) ba f(a,) (b,) 4*x² - 40*x + 114 f(x) =- 1°x - 16*x + 71

Q: (b) Sketch the graph of the cardioids r = 2(1+ sin 0) and r 1- sin 0. Find the area of the region…

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Q: 5 Find the area under the curve y over the interval [0, 1]. (4x + 4)2 Enter the exact answer. area =

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Q: 1. Sketch and find the area defined by y = sinh x, y = e-ª, x =0, x = 2

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find the area enclosed by the curve whose equation is given below: r = 1- 0.6 sin 0

A: Given curve is r=1−0.6sinθ We have to find the area enclosed by the curve r=1−0.6sinθ Area is given…

Q: 1. Find the area of the region bounded by the graph of the equation r = 3 cose. %3D

A: Concept Used: Area in polar coordinates is given by Area=12∫abr2dθ

Q: Find the area under the curve y = 5 over the interval [0, 1]. (4x + 4)2 Enter the exact answer. area…

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Q: 1.Find the area bounded by y=sin(sin x), the X- and x = π axis and the lines x = 0

A: See this solution in below.

Q: 4. Find the area of the region that lies inside the curve r = 1 – sin 0 and outside the curve r = 1.

A: It is required to find the area of the region that lies inside the curve r=1-sinθ and outside the…

Q: Find the area bounded by y = x3 +6, y = x and y-6 www. -X.

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Q: y =x, 4x + y =12

A: Let's find.

Q: Find the area bounded by the curve r = 2-cos 8.

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Q: 1 Find the area onclosed by the Curve r=4-3 sin 0.

A: Area

Q: Question 2 Find the area of shaded region bounded by 3y = x-3 and x = y² + 3.

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Q: 4. a) calculate the area of the area bounded by the Curves TI y=Sin 2x and y sin 2x, OSX<

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Q: Find the area between the curves y = cos(x) and y = sin(x)  from x = -3π/4 to x = π/4. Draw the…

A: To find the area between the curves.

Q: Find the area between y,= 2 sin x and y = 5 cos x over the interval [0, 7]. Sketch the curves if…

A: Topic:-  application of integration

Q: Question 10 Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1.

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Q: Question 4. Find the area bounded by the indicated curves. y =x- 9x, y = 0

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Q: 6) Find the area of the region that lies inside the curve r = 3sin0 but outside the curve r = 2 -…

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Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value…

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Q: Find the area under the curve y = 18 - over the interval [ – 1, 1]. %3D (x + 2)? area = i

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Q: Find the area of the region enclosed between y = 3 sin(x) and y = 2 cos(x) from x = 0 tox = 0.5x.…

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Q: Question 3: Find the area between the curve y = 4 – x² and the line y = -x + 2.

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Q: (b) Find the area of the region that lies inside the first curve and outside the second curve. r = 1…

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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: Find the area under the curve using intervals of 1 unit (X) each Integral - Area Under the Curve…

A: Reimann sum:Take the left point of sub-interval:∫16f(x) dx =∑i=1N f(xi*) ∆x∆x=1∫16f(x)…

Q: 2. Find the area of the region that lies inside both curves = 4 sin(0) and r = 4 cos(0) O +1 2T - 1…

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Q: Л 5л nd the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=-. 4 4

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Q: Use the left-endpoint approximation to approximate the area under the curve off (x) + 1 on the…

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Q: Using a graph, it can be shown that the roots of the equation x V4 – x² = 2 – x are x x 0.81 and x =…

A: Given curves, y=x24-x2,y=2-x and roots of the equation x24-x2=2-x are x=0.81,x=2

Q: %3D Question 3: Find the area between the curve y = 4 – x2 and the line y = -x + 2.

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Q: 12 Find the area under the curve y = over the interval [ – 1, 1]. (x + 2)² area = i

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Q: Sketch the region enclosed by the given curves and solve for the area. y = 2 cos(4x),    y = 2…

A: The given two function are y = 2cos (4x) and y = 2sin (8x).The region enclosed by the curve y = 2cos…

Q: 1 to z = 6 using a Left Endpoint Approximate the area under the curve graphed below from z =…

A: Follow the procedure given below.

Q: y = sin(x), y = 2x

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Q: Find the area under the curve y= 1/(4x+ 2) for 1 ≤ x ≤ 3. Give an exact answer.

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Q: Question 43 > - 0.4x Find the area between the curves y = e' and y = 2.2x +1 from x=0 to x=4 Area =

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: Question 46 Find the volume of the solid that results when the region in the first quadrant bounded…

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Q: (4) Find the area of the region bounded by the curves y = sinx, y = cos I, I = T x = 3π/2. You will…

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Q: Question 16 > Approximate the area under the curve y = with 4 subdivisions. x³ from x = 2 to 4 using…

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Q: Find the area between y= 2 sin x and y = 5 cos x over the interval [0, 7]. Sketch the curves if i…

A: Given: y=2sinx y=5cosx

Q: Use the left-endpoint approximation to approximate the area under the curve of f(x) 3 on the…

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Q: Q1) Find the areas of the regions enclose y = 8 cos x and y = sec2 x, -<

A: Lets find the intersection of the graphs of the function y=8 cos x and y= sec2 x on the interval…

Q: 2. y = ln x, y = 0, x = 0. Solve in two ways.

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Q: Question 2 Consider the curves y = mx and y = x³, where m is some positive real number. Find the…

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Q: Question 16 Find the area of the region bounded by the curves y = 1 and y = x+ 12. **Note: You…

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Q: Question (4): Find the area of the region bounded by the curves: y = cos(nx) and y = -1+ 4x?

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Q: Find the area of the region cut from the first quadrant by the cardioid r =1+ sin 0.

A: The area bounded by a polar curve r=f(θ) in the domain: a&lt;θ&lt;b is calculated using the formula:…

Q: Find the exact area under the cosine curve y = cos x  from x =0 to x=b , where 0&lt;=b&lt;= pie /2.…

A: Giveny=cosx where x=0 to x=b                        and 0≤b≤π2.To find Area of cos x   where x=0 to…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.