6) Sketch the region whose area is given by the definite integral and use geometric formulas to evaluate the integral. 10 (2х + 4) dx

Q: Sketch the region whose area is given by the definite integral. 36- х2 dx -6-

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Q: What is the area of the region enclosed by the curve y=e^x and the lines x=-1 and y=3?

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral   [ 2x 3  - 3…

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Q: an arch of y = sin() %3D

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Q: A water trough has a semicircular cross section with a radius of R = 2 meters and a length of L = 3…

A: Consider the 2 dimensional view of the semi circular tank Let trough is located at 0,0First we…

Q: Use double integrals to find the area inside the curve r = 5sin(e)

A: The given curve is:

Q: By iterated integration, find the area bounded by the parabola y2 = 4ax and its latus rectum.

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Q: Find the area of the region bounded by: r = 6 – 3 sin 0

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Q: 8. Sketch the region bounded by the graphs of the equations and use iterated integrals to find its…

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Q: What is the area of the region bounded by the graph of r = 4 sin 2θ

A: What is the area of the region bounded by the graph of r = 4 sin 2θ

Q: Consider the region bounded by the parabola y=4-x^2 and the x-axis. Set up a definite integral to…

A: Consider the following equation of curves: y=4-x2y=0 Points of intersection: 4-x2=0x2=4x=2,-2…

Q: The area of the region outside the curve r-2+2sin0 and inside the curve r-6sin0 is given by which…

A: given:- r=2+2sin∅ r=6sin∅

Q: . The region is bounded by X = y² and x = 4(y − 2)² Using horizontal rectangles, set – up the…

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Q: 2. Sketch the region whose area is given 25 by the definite integral Jo V25 – x² dx and then use a…

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Q: Find the area of the shaded region. 21) 2- y = 2 2 sin(my

A: Since we are given with the multiple number of question and answered according to the guideline

Q: Find the area between the curve y = x2 + 9x + 14 and the x-axis from x = −2 to x = 0. (Give an exact…

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Q: 4. Sketch the region enclosed by y = 2x – x? and y = 0. Use calculus to find the exact area of this…

A: The solution is given below:

Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: The given integral is,

Q: Sketch the region whose area is given by the definite integral. Then use a geometric formula to…

A: ∫055-x-5 dx The area of the region is,

Q: 10 3. sec x dx

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Q: Find the area enclosed by the given curves y = 8x2 -2  and y = 9 cos(πx). You may find it useful to…

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Q: Find the area of the region bounded by the graphs of the equations               y = cos2 x, y =…

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Q: The definite integral that calculates the area of the region enclosed by the curves y=4 - x² and y =…

A: Solution of the problem as follows

Q: Sketch the region whose area is given by the definite integral. - |x| dx 5. 4. 3 y 3 y 2 -4 -2 y 3…

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Q: Sketch the region whose area is given by the definite integral. The use a geometri formula to…

A: Explanation: Given that,                                        We will graph the function…

Q: 17.Find all points where the curves y = 3r and y = r - r intersect, by solving an appropriate…

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral  tan 5  dx

A: Split tan5x into simpler powers tan3x and tan2x and change tan2x to sec2x-1 and simplify.…

Q: Sketch the region whose area is given by the definite integral. Then use a geometric formula to…

A: Consider the provided integral, ∫-66 36-x2dx Sketch the region whose area is given by the definite…

Q: 4. Sketch the region whose area is given by the integral " sin(x²)dxdy. Label each bounding curve…

A: Let I=∫0π∫yπsinx2dxdyHere, x=y, x= π, y=0,y=π The region is:

Q: (1) Sketch these four lines y = 2x + 1, y = -x, and x = 0 and x = 2. Then use integrals to find the…

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Q: Sketch the region whose area is given by the definite integral. хр y3 Use a geometric formula to…

A: Given query is to find the value of the integral

Q: Use a definite integral to find the area of the region between the curve y = 6x and the x-axis on…

A: Given the curve y=6x. We need to find the area of the region between y=6x and the x-axis on the…

Q: 5. Find the volume of the solid formed when the area in the first quadrant bounded by the graph of y…

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Q: 2) Find the area of the region bounded by two parabolas x = y2 - 5y, and x=3y - y? . Specify the…

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Q: 4) Write a definite integral that represents the area of the shaded region and compute the integral…

A: Given the equation of the line is y=-x+4 Intersection with x-axis: Put y=0 0=-x+4x=4

Q: 8. Sketch the region enclosed by the curves: y = x² – 1, y = 7 – x². Then set up (but do not…

A: Given- y=x2-1 and y=7-x2 To Sketch- The region enclosed by the above curves and then set up the…

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral [ sqrt (e2x   -…

A: Given:     ∫e2x−1dx

Q: Find the area bounded by the graphs of the indicated equations. Compute answers to three decimal…

A: The equation of the curves are: y = x3-3x2-27x+10 y = x+10 To evaluate: The area bounded by the…

Q: 23. Show that the circumference of the unit circle is equal to dx (an improper integral) Evaluate,…

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Q: Use a definite integral to find the area of the region between the curve y = 3x and the x-axis on…

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Q: Find the area of the region bounded by: r = 5 – 4 sin 0

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Q: Solve using iterated integrals. (with graph) Find the smaller area cut from the circle x2 +y2 = 25…

A: The objective is to find the smaller area cut from the circle x2 +y2 = 25 and x=3.

Q: Sketch the region whose area is represented by the definite integral. dx 2 4 Use a geometric formula…

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Q: ind its area using the appropriate definite integral

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Q: Consider the integral dx . For which value of n the error in trapezoidal rule will be less than…

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Q: 2. Sketch a graph of the integrand, shade the region in question and use geometry to evaluate the…

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Q: 23.a) determine the area of the region bounded by x= -y²-3 and x= (y – 2)2 ? (Sketch the region)

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Q: Using integration by parts, the integral f In(8x2) dx is equal to:

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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.