Use an appropriate change of variable to evaluate the double integral: dA, y+x cos R where R is in the first quadrant and bounded by the lines x + y=1 and x + y=2.

Q: Evaluate the double integral : (y – 10x) dx | dy

A: we will integrate first inside the bracket with respect to x taking y as constant and then we will…

Q: 4 sin 3y–6 dy cos 3y

A: We'll evaluate the integral as following.

Q: Use changing order of integration technique to compute eut dy dr

A:

Q: dy using implicit differentiation: 4x°y² – /æ +3y = 57 Find dx %3D O dy -20z'y² + }a¯1/2 8r°y+ 3 dz

A: Given,            4x5y2 -x + 3y =57

Q: Evaluate each of the following contour integrals: sin z 2² +π² dz; |z − 2i = 2 (1) fc fc $c -² sin z…

A: 1) a) Let              ,which  is  analytic inside and on C.Recall Cauchy's Integral formula: Let…

Q: a) By using integration by parts, find the integral Inx dx. b) Hence, find In Vx dx.

A: We have to apply the integration by parts.

Q: Change the independent variable to determine a first integral of the functional: • 02 01 Let v'(1) =…

A:

Q: Find only the limits of the integration of the figure below in the order (dx dy). -SS dxdy *-2-y I=…

A: Solve the equation x=y2 and x=2-y for y to find the upper limit and lower limit of y . Use the given…

Q: sin( 2 tan-1 (x/ 12)) = Select one:

A: Can solve the given function by using double angle formula

Q: Q/ Evaluate the following integrals. S f sec40 tan²0 de

A: W have to find the integral.

Q: Use the substitution technique to determine the following integrals:

A: Important integrals for the question: ∫sec2 x dx = tan x + c ∫un du = un+1/(n+1) + c Other important…

Q: Integrate sinx given integral by 20 2 w5 x= sing the using sin: 1 + si

A:

Q: Determine the required integrating factor: y'=x-2y cot (2x) O sec (2x) O2cos (2x) O2cot (2x) O sin…

A: y' =x-2ycot2x

Q: Find all local extrema for 4 f(x, y): * - 4xy + y.

A:

Q: Use a double integral to fi and y = 3(x+ 1).

A: Given the two curves y=x2+2x+1y=3(x+1)

Q: X3ec 11x tan 11x dx Eveluate the inde ter minate 'integral

A: Evaluate the indeterminant integral  ∫x sec11x tan11xdx

Q: Calculate dwldu and using the following functions: = f(x, y, z) = 3x2 – 2xy + 4z2 x(u, v) = e" sin v…

A: