4) From the graph below 10 -20 -15 -10 10 15 20 -10 -15 a) Use integration to find the shaded area b) Evaluate ſ*,f(x)dx c) Compare between a and b

Q: Evaluate using integration by parts o a) (In 3x dx

A: As per the rules of the company we can only the first question and rest others can be reposted.

Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

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Q: 6. Evaluate: dædy Hint: Use dydx as order of integration.

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Q: 2. Given that f(t) = f cos x cos(t − x) dx, fin integral.

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Q: in integating the function fxcos(3r) de using integration by parts, what would you choose for your…

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Q: Determine h and N to approximate the integral e-t" dt within an accuracy of G 10-5 using the %3D (i)…

A: ∫01e-t2 dt a) Composite Trapezoidal Rule Error=h2b-a12|''Cn ⇒EnTt≤10-5 calculating the derivative;…

Q: The approximation of the integral -2) In (x+2)dr using the two points Gaussian quadrature மாmua is)

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Q: 1DEvalvate the integal usiing Integration by parts. J5 sin ? Cx) dx -ユ Express numbers in exact…

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Q: Illustrate the setting up limits of a double integral?

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Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: In Exercises 1-10, indicate a good method for evaluating the integral (butdo not evaluate). Your…

A: Let the integral be y - y = ∫xsec2x dx                             .......................(1)Using…

Q: Evaluate the double integral (x +y)² sin(x – y) dA for R, which is square with the vertices (0, 1),…

A: Consider the given integral and construct a diagram based on the given conditions.

Q: 4. A cannon ball is shot From the position (0,0,100) with initial velocity (100,120,40) when and…

A: Initial sped of the ball u=(0,0,100) x0=(100, 120, 40) Acceleration due to gravity g=(0,0,-32)…

Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: Use geometry to calculate (without integrating): o V16 – x2 dx Note that f (x) = v16 – x² is the top…

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Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: In evaluating, 2x cos (2x) dx using integration by parts, identify the portion of the integrand to…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: In Exercises 15–22, graph the integrands and use known area formu- las to evaluate the integrals.…

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Q: Mr. Tanveer Ahmed develops an approximate Gauss quadrature formula for integration as [ f(x)dx = c,…

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Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Evaluate using integration by parts. 1)x2 In 6x dx

A: We are asked  to evaluate the integral

Q: Sketch the graph the integrands and use areas to evaluate the integrals. La |(1- l2) dx а. -1 3/2…

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Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its…

A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

Q: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

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Q: 1. Sketch the region of integration for integral by reversing the order of integration. I'sin (y)…

A: Hello, thanks for your question but according to our guidelines I am answering the very first…

Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: 3. Find the area of the region that lies inside both curves: r = sin 0,r = cos 0 0.8 0.6 0.4 0.2…

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Q: sketch the described regions of integration. 1 ≤x ≤ e2, 0≤ y ≤ ln x

A: Given  1 ≤x ≤e2 , 0≤ y ≤ ln x

Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: 3 +h (2x) dx By specifying the type of integr rol, examine it by its convegene explaining

A: We are given an improper integral of the first kind by the following.…

Q: 4 | a sin(3y+ x²)dydx, 2 a) Sketch the domain of integration on an (x,y)-plane. b) Set up the…

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Q: 3. Verify the result shown using 'integration by parts'. | t sin(nt) dt = – -t 1 t cos(nt) + 1…

A: Integral by parts

Q: 10 de . 4+3cose Integrate

A: To evaluate the given definite integral.

Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

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Q: Determine h and N to approximate the integral e- dt within an accuracy of G = 10-5 using the (i)…

A: ii)  Equation is f(x)=exp(-x2).The value of the table for x and y x 0 0.25 0.5 0.75 1 y 1…

Q: In Exercises 19–22, state why it is difficult/impossible to in- tegrate the iterated integral in the…

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

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Q: 5. Find the area enclosed by the inner loop of the curve r = 1-3 sin 0

A: Area Between Functions With Integration: The interval of the inner loop of the given polar curve is…

Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

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Q: 7. Use contour integration to evaluate (a) dr x²+x+1² de (b) 3+2 sin

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Q: 5. (a) ( If ryz² + x²yz + ry²z = e*v², compute . (b) Let f(r,y) be some function. Set up the…

A: (a) The equation given in the question is: We need to evaluate  This represents the derivative of…

Q: In The value of the definite integral flm 12 √ex - 9 dx is in the form F(b) - F(a), where a JIn 9…

A: To evaluate: ∫ln⁡9ln⁡12 ex−9dx Let I =∫ln⁡9ln⁡12 ex−9dx Given: ∫ln⁡9ln⁡12 ex−9dx = c3-dπ Let ex−9=…

Q: (2х? + у)dx + (x?у — х)dy %3D 0

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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.