By sketching the graph aud using Integration, Find the ared of the regim bounded by tue paraboka (4-10)- 化メ-4) and tue straight line -4=6,4=D14CA=8

Q: The exact value of the integral [In[I + x) x²]+ 2dx is-0.3521. Evaluated this integral (a) by the…

A: (a)∫12x-x2+lnx+1+2 dx using n=4 trapezoids.The trapezoidal rule states…

Q: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: by using the double integration, find the area that lies inside the curve r= (8cos e) and outside…

A: Given: The curves r=8cosθ    and r=4

Q: Use integration tables to find or evaluate the integral.

A: We have to evaluate the integral: ∫x4+5x2dx Assuming, t=4+5xx=t-45 Differentiating,…

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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Q: Evaluate the integral using tabular integration by parts. 4 x° V2 x + 1 dx +C

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Q: The value of the integral Vx dx computed using Trapezoidal rule with 2 subintervals is (Rounded upto…

A: The trapezoidal rule uses the area of the trapezoids to approximate an integral. Using the…

Q: Use integration by parts to evaluate the integral: fin(2) - V/="da = ,11

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Q: The error is numerically computing the integral | 1 dx using the +4 trapezoidal rule with two…

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Q: Evaluate the integral using tabular integration by parts. 7 x V2 x + 1 dx

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

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

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Q: Evaluate the integral using tabular integration by parts. |2 V2r +1 dr = V2 x +1 dx +C

A: First integrate root terms separately as I have done step by step with all explanations...hope now…

Q: By exchanging the order of the integration, the evaluation of siny dydx y klea

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Q: Evaluate the integration: r sin(20)drd0 Over the area in the first quadrant bounded between two…

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

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Q: The path C is a line segment of length 13 in the plane starting at (4,5). For f(x,y)=5x+12y,…

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Q: The region D is bounded by the curves y = 5, and y = 5x². Which of the following can be used to…

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Q: Find the area of the region (as shown) in two ways. a. Using integration with respect to x. b. Using…

A: a) Substitute 0 for y1,1 for y, 0 for x1 and 1 for x in m1=y-y1x-x1 to obtain the slope of the first…

Q: Sketch the region D of integration, and then evaluate the integral by reversing the order of…

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Q: Evaluate the integral using integration by parts. 40 sec 20 do

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Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Use an appropriate change of variable to evaluate the double integral: cos dA, R where Ris in the…

A: Given integral is  ∫∫Rcos(y-xy+x)dAR is the region bounded by x+y=1 ,x+y=2 in the first quadrant.

Q: Sketch the region of integration rev 1 4-2x a) S [ydydx 0 2

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: To obtain an 0(h) approximation for an integral I using Romberg integration, we start by…

A: We proceed to upto third approximation to get the integral of accuracy h^6

Q: First make a substitution and then use integration by parts to evaluate the integral. ecos t sin 2t…

A: The definite integral to be solved is  ∫0πecostsin2tdt

Q: Sketch the curve ĕ= E Set uf, buz de not evaluale, an integral for the are- length of the Rurve from…

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Q: Find the points of discontinuity of the integrand on the interval of integration, and use area to…

A: The integral is discontinues where the function is not defined

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: ydy (y–1)*

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Q: Sketch the region of integration described by 2x cos(x) dy dx, write an equivalent integral (or…

A: When we integrate a function with two variables over a rectangular region, the conception of double…

Q: 5x

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Q: Evaluate the integral using integration by parts. 2x dx (5x2 - 12х) е 2х

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Q: Find the area bounded by axes and line 7x + 5y = 35 using any differential strip

A: Explained  below...

Q: A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration…

A: Introduction :

Q: sec? (4x)(3 – tan(4x))³dx

A: Given integral is,  ∫sec24x3-tan4x3dx. Substitute t=3-tan4x.…

Q: 5xt AK fue?

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

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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: Evaluate the integral by making an appropriate change of variables. 2 sin(25x2 + 36y2) da, where R…

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Q: The area bounded by the small loop of the limaçon r = 1 – 2sin0 is given by the definite integral

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Q: The area bound by the curve y^2 = 12x and the line x = 3 is revolved about the line x = 3. What is…

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Q: Evaluate the integral using tabular integration by parts. |(4 2 – x + 2) e* de +C

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Q: Evaluate the integral using tabular integration by parts. 1 | 7 x° V2 x+1 dx (2x + 1) (35x – 15x? +…

A: Given,            ∫7x32x+1dx

Q: Using tabular integration, the integral In 2 S™ (-2x + 1)e²x dx is equal to

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Q: Evaluate the integral by making an appropriate change of variables. 7 sin(25x2 + 25y²) dA, where R…

A: Double integral evaluation, conversion to polar coordinates

Q: 3. x+1 dx

A: let I=∫5x32x+1dxput 2x+1=u2x=u-1x=(u-1)2and  2x+1=udifferentiate w.r.t.…

Q: (a) In(4x) dx

A: Integration by parts:  ∫f(x)g′(x)dx = f(x)g(x) −∫f′(x)g(x)dx

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.