Apply Green's Theorem to evaluate the integral O(- 3y dx- 3x dy), where C is the triangle bounded by x 0, x+ y 1, and y 0. C O(- 3y2 dx- 3x? dy) =(Type an integer or a simplified fraction.) %3D

Q: Evaluate the integral fa* (2* – 11)"dz, dx, by making the appropriate substitution: u = 11). 24 dx =…

A: ∫x3x4-1124dxSubstitute u=x4-11du=4x3dxdu4=x3dx

Q: For the integral xe2x) dx what is u? Note: no space between symbols in your answer

A:

Q: raluate the double integral R 3ædA where Ris the triangle with vertices (-1,0), (0,1) and (1,0).

A:

Q: Consider the integral dx . Using u-substitution, what is the appropriate u and du? -2x 3e 2t 2e

A:

Q: 7. Evaluate the integral (16 – 2? – y?) dV where E is the solid hemisphere x² + y² + z² 0

A:

Q: Evaluate the triple iterated integral. 2/2 L7 xyz dx dy dz 0 Jo J-1

A:

Q: Use symmetry to evaluate the double integral. 4xy 1+ x2 dA, R= {(x, Y) | -4 s x s 4,0 s y s 1}

A: When the upper and lower limits of definite integrals become same, the result is zero irrespective…

Q: e* dx? e* – e -> What is the integrable form of du ? du

A: Explained below

Q: satis ties the given integral. tind the derivanive of yat (0,0) e de =xy (0.0) dy

A:

Q: Calculate the double integral of f(x, y) = over the triangle with vertices A = (1, 10), B = (7,16),…

A:

Q: Consider the triple integral I - f L, S dzdydx. The value of I is:

A: In this we have to integrate this triple integral problem three times with respect to z, y & x

Q: Evaluate the iterated integral. 1 13 4ze x* dy dx dz

A: The given integral is: I=∫12∫01∫0x3 4ze-x4 dy dx dz

Q: Area = 2c 27 dx

A:

Q: Verify Green's Theorem by evaluating both integrals ƏN [ 1² dx + 2² dy - [ ] (™N - OM) a dA ax ду…

A:

Q: Evaluate the integral / cos[3 +1/(z – 3)] dz, where Y is the unit square with corners at 0, 1, 1+i e…

A: Given; ∫γcos3+1z-3dz Where, γ is the unit square with corners at 0,1,1+i e i

Q: Use u-substitution to evaluate the integral. 3 + 5 Vx dx 3 2 + 5 Vx dx =O

A: Given query is to eveluate the integral.

Q: evaluate the triple iterated integral.

A:

Q: Evaluate the integral dV, where E is the region below the paraboloid E 2 + y? + z = 7 and above the…

A:

Q: Verify Green's Theorem by evaluating both integrals Lv dx + x* dy = / dA əx for the given path. C:…

A:

Q: Evaluate the iterated integral. 9. 2ye-X dy dx

A:

Q: 20. Re-write the triple integral =9 dz dy dx so that dV = dx dy dz, then evaluate the triple…

A:

Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: (c) Consider the following integral I =ff (x + xy - xy — x² − y²) dA, - - D where D is a rectangle…

A:

Q: 5. In antidifferentiation, the formula J x" dx : + Cis valid if? (n+1) C. ne {0,1,2} A. nER 6. In…

A:

Q: Use inversion order to the ff integral, the limits of the innermost integral must be a. √x to x b. X…

A: ∫01∫y2y1-x2dxdylimit of y is from y=0 to y=1limit of x is from x=y to x=y2draw region bounded by…

Q: Apply Green's Theorem to evaluate the integral P (4y² dx + 4x² dy) , where C is the triangle bounded…

A: See the details solution in below

Q: LUOnsan For the given integral xcos (2x2+7) dx what is du? Note: no space between symbols in

A: In the above integral du is 4x dx.

Q: 3. Use the Fundamental Theorem of Calculus Part 2 to evaluate the integral, or state why the…

A:

Q: Evaluate the iterated integral. 7 8 !! //(? + y² + z²) dx dy dz -6 0 0

A:

Q: Evaluate the triple integral and confirm that 2 2 dx dy dz = = In 35, where D is the rectangular box…

A: We will prove the given statement .

Q: sec 2x In evaluating the integral dx, using the appropriate formula, the du = M. V1+tan 2x •1/2…

A:

Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

A:

Q: What is the definite integral representing the area of the given region below? A. A= (1,1) В. А-D…

A: Area of a region bounded by two curves x=f(y) and x=g(y) is given by, A=∫ab |f(y)-g(y)|dy where a, b…

Q: Which of the symbols below denote the operation of antidifferentiation? c. Sf(x)dx = F(x) A. F(x)) =…

A: Since, you have posted 3 questions. We"ll solve first two questions, because 3rd one is incomplete…

Q: Evaluate the iterated integral. 2. r1 7ze dy dx dz Jo Jo

A:

Q: Verify Green's Theorem by evaluating both integrals an aM dA y² dx + x² dy = |/ əx ду for the given…

A:

Q: the double integral dg dx Evaluate

A:

Q: The value of the triple integral (r + y)dzdydx

A: To evaluate  ∫01∫0x∫0x+y(x+y) dzdydx Formula used ∫dx=x∫xn dx= xn+1n+1∫abf1(x)= f(b)-f(a)

Q: Let E {(x, y, 2) E R³ : 1 < x < 2, 1 < y < x², xy < z < 1}. Write the integral dV in the order dz dx…

A: Given,    E = (x, y, z)∈R3: 1 ≤x≤2, 1≤y≤x2, xy ≤z≤1Then ∫∫∫E dV =∫y=1x2∫x=12∫z=xy1 dz dx dy

Q: a²f, a2f ax ay2 ду? f(x, y) = In(x2 + y?) + tan-1() A- Show that = 0, where B- Evaluate the integral…

A: Dear students you have asked multiple questions. As per our policy your first question will be…

Q: Verify Green's Theorem by evaluating both integrals y dx dA ay dy ax for the given path. C: boundary…

A:

Q: c) Evaluate the integral e* (x + 1) - dx, VI – x² using 3-points Gaussian quadrature.

A:

Q: use a computer algebra system to evaluate the triple iterated integral.

A: Using a computer algebra system we get

Q: Evaluate the triple iterated integral. 2 4 xyz' dx dy dz Jo Jo J -1

A: Here we have to solve the givne triple integral I=∫02∫01∫-14xyz3dxdydz

Q: Evaluate the double integral x* dA, where D = {(x, y) : 1 < x < e,0< y< In x}. %3D

A: The solution is given as

Q: What is the value of the integral (3z-2) with respect to z from z=-i to z=? 0 a -i b 1 .c O -1 i…

A:

Q: Consider the integral dx . Using u-substitution, what is an appropriate u and du? 2e -2x A u=/3 e2*.…

A:

Q: 1. Evaluate the integral: , xe*+y* dV where B is the portion of the unit ball x? + y? + z? <1 that…

A:

Q: Consider the following. (In(x)) , dx The process of evaluating this integral can be started using…

A: See the details solution in below

Q: 2- Assume that x, y e R and z = x + iy E C and answer the followings. Calculate the reel integrals…

A: Consider the given figure in the question. We have to evaluate I=∫x=0∞1x3+1dx in the given contour…