- SxS Write an integral for the area of the surface generated by revolving the curve y = cos (3x) about the x-axis on K |co

Q: 2.0 Hence, evaluste Se? cosz de to 3 decimal places. CoS I

A: According to question given that ∫01ex cosx dx

Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

A:

Q: Write an integral for the area of the surface generated by revolving the curve y = cos(4x) about the…

A:

Q: Which one of the integrals below represents the area of the region that lies inside the curve r = 3…

A:

Q: Set up an integral for the area of the surface generated by revolving the given curve about the…

A:

Q: Set up an integral to find the area of the surface that is obtained by rotating the curve y = V4 –…

A: Here, y=4-x2, 0≤x≤1 is positive and has continuous derivative on 0≤x≤1. So, the surface area of…

Q: The area of the region outside the curve r=2+2cos0 and inside the curve r=3 is given by which…

A: Intersection points between two curves; r = 2 + 2 cos θ and r = 3 3 = 2 + 2 cos θ 1 = 2 cos θ cos θ…

Q: V2y? – 3 dy y?

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. xy dy dx = 0.

A: We have to calculate the integral ∫01∫x2xxy2dy dx

Q: 7) (g) Set up and evaluate the definite integral for the area of the surface generated by revolving…

A: we use integration formula for area of surface rotating about x-axis..

Q: let J(x) = farctan(Va + 3)dx – [(x + 4) arctan(Vx + 3)]. Let C be the constant with respect to this…

A: Please refer the attached image for complete solution.

Q: 5. Find the surface area when the curve x-sint, y=sin?t is revolved around the x-axis -just set up…

A:

Q: Evaluate the integral. integral y e 2y dy

A: Evaluate ∫ye2ydy

Q: 3) Write the integral that equals the area of the surface formed by rotating the curve x = 1 + 1s y…

A: Write the integral that equals the surface area of the given curve rotating about x-axis

Q: Evaluate the indefinite integral. 15y dy J(y – 4)(y² + 4)

A:

Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. dy dx (xy + 1)

A: We need to evaluate the integral- ∫04∫01x(xy+1)2dydx Here integral is with respect to both x and y.…

Q: Which of the following integrals will find the area of the surface generated by revolving the curve…

A: fx=x3 is a polynomial function. It is continuous in the interval 0,3.

Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

A: Solution: The objective is to find the area of the surface

Q: Use substitution to find the indefinite integral

A: Given ∫1xlnxdx

Q: Find the area above the curve y=Inx in the lower half-plane between x-0 and x=1. YA y=In x 0. O a. 1…

A:

Q: let J(x) = f arctan(Vr + 8)dx – [(x + 9) arctan(Vr + 8)]. Let C be the constant with respect to this…

A:

Q: Q2: Find the surface area generated by rotating for y = x² - ln(x) for x = [1, 2] about the y-axis.

A: We need to find Surface area.

Q: Find the following indefinite integral. |(4cos(y) – 2sec(y)tan(y))dy

A: Explanation of the answer is as follows

Q: Q5. Use a double integral to evaluate [f sin 0 dA where R is the region in the first quadrant that…

A:

Q: Consider: S (x?, v>dr, C: r(t) = (sint, cost), te[0,1] Which one of the following "regular"…

A: Given ∫Cx2,ydr and C:rt=sint, cost i.e. xt=sintyt=cost

Q: Set up an integral for the area of the surface generated by revolving the given curve about the…

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. dy dx = (xy + 1)?

A:

Q: Evaluate the integral by making an appropriate change of variables. 9 cos( 3 (Y-X)) dA where R is…

A:

Q: Evaluate the integral. NOTE: Enter the exact answer. dy dx

A:

Q: Consider the following curve. y = x, 0sxs 3 Set up an integral in terms of x that can be used to…

A:

Q: Evaluate the double integral of the function over the rectangle cos(2x) sin(y) dA, R = 0, 0, 2.

A:

Q: 3) Write the integral that equals the area of the surface formed by rotating the curve x = 1+ 2y2, 1…

A: Recall: If the curve is given by x= g(y) ,c≤y≤d and rotated about the x-axis , then the area of the…

Q: Suppose we want to find the area enclosed by the curves y1 (z) = sin(z) and y2(z) cos(z) %3D %3D to…

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: Determine a definite integral that represents the arc length of r = 6 cos(0), 0 <0< de 0. 下一2

A: Arc length

Q: Evaluate the iterated integral below. 1 S. * S'y cos 0 0 y cos (x) dy dx

A: Given, ∫0π4∫01y cos(x)dy dx

Q: The area of the surface obtained by revolving the curve x= Vy+4 for a-4.)

A: We have dxdy=12y+4

Q: Consider the function y (x) = 1 + ex / 2, from the point (0,2) to (4, e2). Set up the integral that…

A: Given that: y(x)=1+ex/2

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: y=16-x2,  -1≤x≤1 Differentiating with respect to x, we get…

Q: Which ONE of the following integrals correctly represents the area of the surface of revolution…

A: giveny=ln(x5)rotation about x-axisA=∫152πyds

Q: D. Set-up the definite integral that will give the area of the surface generated by revolving the…

A: D) Given arc is y=2x⋯⋯(1)   Arc revolving from x=0 to x=2. a) To find: area of the surface revolving…

Q: Use an appropriate change of variable to evaluate the double integral: co where R is in the first…

A: Given the region:

Q: 3(sin y- cos y) chy cos y

A: First we use (siny - cosy) 2 =sin2 y + cos2 y -2sinycosy Then using u substitution let u =sexy +…

Q: Evaluate the line integral along the curve C. (3x² + y²) dx + 2xydy, C: x = cos f, y = sin 1, 0≤1≤ 2…

A: Given integral is ∫C3x2+y2dx+2xydy , where curve C:x=cos(t), y=sin(t), 0≤t≤π2 We need to find the…

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral  tan 3  (  1/z)…

A: To integrate: ∫tan31zz2dz Let substitute t=1z Differentiating both sides, we get dtdz=-1z2-dt=1z2dz…

Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

A:

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: Consider the given integral as  2π∫-5581-x2dx

Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

A: