Integrate the following: ,S (x4 – 5æ³ + 6) dæ - 1. So(1- r)*dz su(1– 2.

Q: Evaluate the integral. - 1 y° - 7y° dy У -1 9* У – 7y° dy = -Ty - 4

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Q: Evaluate the iterated integral. 2 1T 2 - 2y3) dx dy

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Q: From 12ty²<³dz « dy dx, which of the following is a correct partial evaluation of the definite…

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Q: Evaluate (3 t + 5) cos () d+ using integration by parts .

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Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: In (rle) sec³x (2– sec²x)«ma/2)sec³x What should be the value of A for dx to be integrable using the…

A: we have to find the value of A.

Q: 2 c2 Reverse order and evaluate the integral S, 2y2 sin(xy) dydx

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Q: Calculate the double integral. 3xy? dA, R = -{(x, m10 sx 5 3,-25 ys 2} -2 s ys2} .2 + 1

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Q: Evaluate the iterated integral. T/4 1 Tv cos(x) dy đx

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Q: Evaluate the integral VI- 1 /1 dy dx. – x² – y2

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Q: Find the double integral ∫∫R(2x^2−5y)dA, where R=[−1,2]×[1,3].

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Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-4

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Q: Evaluate the iterated integral. * 2y (6 + 8x2 + 6y²) dx dy

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Tind dʻz of z- In (xy) Find d²z z - In (xy)

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Q: Evaluate tne following double integral ! VI- 2 (2 + y)* dyd.r. -1 0

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Q: Evaluate the iterated integral 2y dy dx 2 x +1

A: on solving this we get the

Q: C for the con

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Q: Evaluate the double integral : 9. dy dx 0, 22

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Q: Evaluate the integral. ,3π/2 20) 6 cos 2x dx T/2

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Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-2

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Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

Q: If I, = Sx" cos x dr, by using integration by parts, prove that In = x" sin r + na"- cos r – n (n –…

A: We use integration by parts to show given condition.

Q: Evaluate the iterated integral. *7/3 '5 y cos(x) dy dx

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Q: Evaluate the integral. 2 | 7t sec -'t dt 2113 | 7t sec - 't dt = 2113 (Type an exact answer, using t…

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Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

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Q: Evaluate the iterated integral. (3x - 2y) dy dx 1 Jo

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Q: Evalate jsinty)hube where 2 05ys1,05xsy. a) 1-cos(r) b-costr)) 9-cosd) osd) d) 1-cos(l))

A: Change of variables:             ∫x1x2∫y1y2f(x,y)dy dx=∫y1y2∫x1x2f(x,y) dx dy.

Q: Calculate the double integral. 9x sin(x + y) dA, R = 9v 3

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Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

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Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

Q: In evaluating / x(4 – x)ŝdx , if we use the substitution that u = 4 – æ, then what will be the…

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Q: c) Evaluate Ssin 3.xcos 4x dx by using integration by part.

A: Here we have to find            ∫ sin 3x cos 4x dx Integration by parts formula is          ∫ uvdx =…

Q: Evaluate the double integral. 8xy2 dA,    D is enclosed by x = 0 and x = (4-y^2)^1/2

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Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy d.x - x+4

A: Let's find.

Q: Q1\ Differentiate the following (c 1)2xsin-13x 2)y = In *+1 Vx-2 %3D 3)y %3D sin-1 2x

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Q: For n EN,n> 1, making a suitable variable change in the integral sen"r cos³ xdx, ,it is obtained…

A: Explanation of the answer is as follows

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

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Q: Apply the techniques of Example 7.1.5 to the evaluation of the improper integral 8 dx 1 = (a) Let…

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Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

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Q: Evaluate the double integral: cos(y') Vy3 dy dx.

A: The solution is given as

Q: xcosr (i) Find the Cauchy principal value of the integral dr. ² + 4x + 8

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Evaluate the in tegral (x+ 2y) dy

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Q: Evaluate the integral: -2e 2е π/3 ₁² /³ tlnu tans ds du dt 0

A: In this triple integral we first integrate with respect to 's' then with respect to 'u' and in last…

Q: 15. The area enclosed by r=2– 2 cos 0 is: А. В. С. 9Tt/2 D. 9t/4

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Q: Evaluate the iterated integral. 6. I (8x - 2y) dy dx | 1

A: Given: ∫19∫0x8x-2ydydx

Q: Evaluate the iterated double integral 2 b.) √ √ ² sinπTy ³ dydx

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…

Q: (х3 + 2у — z + 3) dxdydz 0, 1 2

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