Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6 y dx + 3x*dy, where Cis the square with vertices (0, 0), (3, 0), (3, 3), and (0, 3) oriented counterclockwise. 6 y²dx -81

Q: 21 · 8* cos (8*) dx =

A: ∫21*8xcos(8x)dxSubstitute u=8x→dudx=ln(8)*8x→dx=1ln(8)*8xdu=21ln(8)∫cos(u)du

Q: A parametric curve is given by the equations: x (t) = 3 – t, y (t) = 2t, 0 <t < 3. After eliminating…

A: The given parametric curve is  x(t) = 3-t, y(t) =2t,   0≤t≤3 Here,  parameter is t.   We have to…

Q: what is 2x2

A: 2×2= 4

Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: Describe several types of line integrals and discuss how they are related.

A:

Q: Determine a, and as for each arithmetic sequence. See Examples 3 and 4. 29,. 24. -3, -7, -11,... 25.…

A: Since, the student has mentioned to solve only question number 24, so we are solving accordingly…

Q: Find all rational zeros of the polynomial, and then find the irrational zeros, if any. Whenever…

A: Solution:

Q: r(t) = 4 cos(t)i+4sin(t)j; t = 3 /3 1 2/2' 2/2 -V3 2/2' 2/2 1

A:

Q: Evaluate the definite integral. Si f (x) dæ, f (x) =4"-(7a+ 13)/a?

A:

Q: 2. Find any excluded values, then solve the following equation: 1 1 I 2+2 IN

A: We have to solve the given equation 1/(x-1)+1/(x+2)=1/2

Q: Suppose f(5) = 9 and f'(5) = - 3. An object moves along the curve y – 3x? f(x) – 5x = 649. For an…

A:

Q: Evaluate the definite integral. NOTE: Enter the exact answer. •3 ti + ti dt

A:

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A:

Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: Find the centroid of the given region. y = 2-x? y = x A (3/22,45/61) В) (5,15) c) (5/14,38/35)…

A: Centroid is x¯,y¯ , where, x¯ = 1A∫ab xfx-gx dx  and y¯ = 1A∫ab 12 fx2-gx2 dxand A = ∫ab f(x)-g(x)…

Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x – z)i+ (y – x)j+ (z – y)k - across…

A:

Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. =…

A:

Q: Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly and…

A: To calculate ddtr1t·r2t and ddtr1t×r2t first by differentiating the product directly and then by…

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +9 1 lim tto 9t2 + 10' 7t |(?,?)

A:

Q: Is there a number a such that the following limit exists? (If an answer does not exist, enter DNE.)…

A: Given;  limx--2 (4x2+ax+a+12)/(x2+x-2).

Q: · ln(1+x) a) dx f (1+x)7 u= du = b) f(2x + 1) tan-¹ √√x dx U= du = c) f x² sin(2x) dx U= du = dv =…

A: I have performed integration by parts for the part a) and for the rest I have mention the u and dv…

Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt the product directly and…

A:

Q: H.W: find the angle between the planes x + y = 1 and 2x + y- 2z = 2

A:

Q: dx 6x + x2

A:

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: Find your answer below

Q: Describe the graph of the equation. r = 8 sin 5t i + 8 cos 5t j O Itis a circle of radius 8 in the…

A:

Q: Confirm that the force field F(c, y) = 2xy³i + 3x?y?j is conservative in some open connected region…

A:

Q: 37. If R is the total resistance of three resistors, connected in par- allel, with resistances R1,…

A: If R is the total resistance of three resistors, connected in parallel, with resistances R1, R2, R3,…

Q: (a) Put a pair of brackets on the left hand side to make these statements correct. 17-2 + 8-4- 11 -…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A:

Q: Chain rule and implicit differentiation Suppose that F(r, y, 2) = 0 defines z as a function of z and…

A:

Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) dx 2x

A:

Q: Use the Divergence Theorem to find the flux of F(x, y, 2) = (a* – e)i+ (y³ + sin z)j + (2³ – cy)k 3…

A:

Q: me origin is 6i + 8j, then the me direction of a = 3i + 4j at

A:

Q: Calculate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A:

Q: Find the limit. lim (t i – 4 j + t k) lim (t i – 4 j+? k) i i+ i j+ i k

A: The given limit is; limt→9t i-4 j +t2 k

Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti + t°j dt

A:

Q: r 0 18. common to = 3 cos 0 and 1=1+cos (

A: Given; r=3cosθ and r=1+cosθ

Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A:

Q: Integrate on of these partial fractions. (choose any)

A:

Q: 4. x = VI - i , y = t³ – 3t

A:

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

Q: ven the equation below, find dr 30x² + 5x¹5y + y¹0 = 36 I w, find the equation of the tangent line…

A: We will find the tangent equation and slope.

Q: 7) Determine the total area bounded between the function y = 1 – x between 1 and 1. -

A:

Q: Vertical and Horizontal area of the plane region y=2x^2+1 and y=x^2+5

A:

Q: 1. ++x xp. dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4. Evaluate: lim (a² + e-*)(= cac r) エー→0+

A:

Q: a) Find a polynomial P(x)= a + a₁x+0₂2² +03x³ +ay 20² +a5 205 of degree 5 such that as = 1, and…

A:

Q: Solve for the Maclaurin series. You can write the first 5 terms or express in summation notation…

A: Maclaurin series is expansion of function at x= 0.

Q: An object moving along a horizontal coordinate line has directed distance s(t) = t - 6t2 + 9t + 11…

A: s(t)=t3-6t2+9t+11 Differentiating with respect to t s'(t)=ddt(t3-6t2+9t+11)=3t2-6*2t+9+0=3t2-12t+9…