Evaluate and simply S x(x2 – 3)8 dx. (Show what is u and du)

Q: N. R dy dx where M,N, P.Q and R are algebraic expresions.

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Q: If k> 0 such that O St the above 4* dx = 3 then k = 2ln 2

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Q: Let fr)-ll for x0, then/(x) is Selact one A-1 * CNone of these DNot defined E1 a.

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Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: C. If w=f(x,y) and x = r. cose, y=r. sine. Prove that aw ar aw +1 (2001) = fx² + fy²

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Q: Use Green Theorem to Evaluate yx'dx – x*dy where C is left half of x² + y = 25 77.7704 O 78.7712 O…

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Q: Evaluate the indennite integrais below. Use U-Sub propi (a) | x°(4x° – 1)°dx (c) 10 cos“(6) sin(0)d0…

A: a ∫x24x3-16 dx    Let 4x3-1 = u

Q: F Recaghi2e f the fehctioh abe evola ar ood fex) =X+|

A: Given : fx = x+1

Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

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Q: x3+y3 x+y If u = = In ди X ?x In ( ди + у ду then find the value of ?

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Q: H.w using par sevel? identity Let fex) e show +ha t(xdx (x41)2 %3D - Fsls):

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Q: Use the technique that we went over in class to find "u", "V", and "du". u = 3x du = 3 dx V=-x2 u =…

A: u=7x Therefore du = 7dx

Q: Exercise 4. sin(3z) Let f(z) : and C: |z| = 1. Then ſ. f(z)dz = z?(z-n) а. 0 b. Злі с. —6лі d. None…

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Q: k< -4 In?(kx + r) di In (kx + t): dx Find k so that kx + T

A: As from the chain rule, ddxf(g(x))=f'(g(x)).g'(x)     .....(1) If g(x)=kx+π⇒g'(x)=k And if…

Q: Evaluate p xy*dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,3), and (0,3)

A: *Concept:- Use Green's theorem.

Q: [ u#(u – 1)"-1 đu (1+x!/n dx = n

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Q: 25 - x2 In dx , if we let u=V 25 – x2 , then udu = - xdx. A True B False

A: On solving this we will get

Q: 21. x'e2* cos x dx (Hint: Let u = x')

A: ∫x5e2x  cosx dxIntegration by parts∫f dg=fg-∫g dfwheref=x5 cosx, dg=e2x dxdf=-x5 sin x dx,…

Q: Which one is not equal to o V(x + 3)³ dx. lim, 100 E i=n-1 (음 + 3)3. O lima-00 1ri=n-1 Li-0 2i+1 +…

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Q: du k Ət u with ди (0, t) = 0, du (L, t) = 0, and u(x,0) = f(x). Əx²

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Q: Let h(z, y) = eVv-zi 1. (a) Evaluate h(-2, 5). (b) Find and sketch the domain of h. (c) Find the…

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Q: Q1. If w = f(u, v), u = cosx and v = sinx, show that: d?w v2 fuu + u² fov – 2uv fuv - ufu - vf dx2

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Q: S°1- (In x)2 dx=? If u= In x, then e A B L (1- u)du .2 © (1-u²)du

A: Given: I=∫ee21-lnx2xdx   ....1

Q: m!n! If m, n e N, then prove that ,, dx = m.n (m+n+1)!

A: A detailed solution is given below.

Q: az Find when u = 0 and v dv 117 if z(x, y) = sin x + cos y, x = u •v, and y =u + v.

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Q: Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² funu + u? fov – 2uvfuv – ufu – vfp %3D…

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Q: Use the substitution u = csc x- cot x to evaluate csc x dx (see ample 6).

A: We will evaluate the given integral by using substitution method as shown below

Q: m+n If x"y" = (x+y)*** m, n d'y prove that = 0 .2 dx?

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Q: az az and du #6. Use the Chain Rule to determine given that av z = x sin (y? – x) x = 3u – v?, y =…

A: Solution:-

Q: g(x)]dx, (b> a), for all f, g € X. Show that (X, d) is a me

A: Matric Space

Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: az az Let z = sin(x? - y²), show that x y = 0. %3D %3D ax ay

A: Given function is  z=sinx2-y2

Q: F Given: ABCX is a O: DXFE is a C. Prove: ZB = LE X, D

A: Given that, ABCX is a parallelogram and DXFE is a parallelogram. We have to prove that, &lt;B =…

Q: Xarctonx dx which of the following îs the Va lue 1+x2 2) of the întegral în the meaning of Riemonn?

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Q: =Xtanx dk, Prove that ="IH (n+1)I,+(n-1) -1 T 1 2 n

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Q: Let C: |z – i| = 3 and I = $. e 5z dz. Then 22 %3D |= 4ti |=0 |= 6ti None of these |= 10ti

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Q: Given f(r, y, z) = In(x² + y? + 2²), show that af, f, s dy? %3D dx² x² + y? + 22

A: The given function is fx,y,z=lnx2+y2+z2........(1) To show: ∂2f∂x2+∂2f∂y2+∂2f∂z2=2x2+y2+z2

Q: a) (dx pcG) V ZxqG))3x (pG) V96), Pore this bis the converse of t he implication above correct!

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Q: Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² fuu + u?fov – 2uv fuv – ufu – vfp dx2

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Q: Iff, g e R(x) on [a, b), prove that f? dx + g? dx 2 2 Ifg | dx.

A: Given that, f, g∈Rx on [a, b]We need to prove that∫abf2dx+∫abg2dx≥2∫ab|fg|dx

Q: Evaluate F di where F = (4z, 0, - z), and C is given by 7(t) = (t, sin(t), cos(t)), 0 st<R

A: Use parametric to solve

Q: Let f(0) = 6 and ƒ(1) = If ) dx In then a =? %3D 8.

A: given that f(0)=6 and f(1)=94 and ∫01f'xfx dx=lna8  find a

Q: S0scies 1CAR is inscribedin a E = 130°. %3D Finc: 12. iaCR 13. RC 14. mÃC 15. mAR

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Q: x cosx dx Evaluate with Simpson's 1/3 rule using two, four, and six panels.

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Q: dy a. Find of the following. dx 1. у%3D 4u? + би — 2 and u — 4x? + 8х + 1 - 2. у%3D uVu +1 and u %3D…

A: Here we have to find dy/dx.     Note : As per our company guidelines we are supposed to answer only…

Q: pt 6.1.6 For f(x,y) = In x+y°, find f( e2,8). f(e?.8) = D %3D

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Q: UCe the Vmit de fi miおもn of rhc aefrile へとgral, im ; fcxi)x - 5fしょsdx」 to prove hat ハう fex) dx= -…

A: Prove ∫abf(x)dx=-∫baf(x)dx using the limit definition of the definite integral as follows. By limit…

Q: Ⓒ'Evaluate Sot So Sox sing ²sin y dy dz dx tim of the

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Q: 25— х2 -dx , if we let u=V 25 – x2 , then udu = – xdx. A True B) False

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