Q2// Evaluate the integral for the following Vectors function (two only)? 1- [(4 sin(3r)i + 4te j + (2t + 31)k )dt In (sinh x) 2 - ( ,. tanh x 1 -k )dx 1- sin x i + V1 - x

Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

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Q: b) (2 points) Find the exact value of the following integral. Show all your work. 1 5 + 2x + 3 4e" )…

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Q: Q2:A/ Evaluate the integrals 1 sec²(eVx + 1) dx J Vxe-V

A: Given: ∫1xe-xsec2ex+1dx Consider, u=ex+1, du=ddxex+1=ex+1ddxx+1=ex+12xdx

Q: If u'(x) between u(x) and v(x). v(x), write a statement involving integral sign giving the…

A: Given: u'(x)=v(x)we know that u'(x)=du(x)dxdu(x)dx=v(x)du(x)=v(x) dx

Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

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Q: The differential of the function f(x,t)= e cos(2 tt) at the point (x,t)= (0,1) is given by -2dx +2…

A: Topic- Application of derivatives

Q: (x + siny - cosy + 1) dx + (xsiny + xcosy)dy = 0

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: Integrate the function. dt 4-R 412 V4 -2 4t sin1 4t + C 4t - + C

A: Consider the given integral: ∫1t24-t2dt Here, the objective is to evaluate the given indefinite…

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (3e' cos t)…

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Q: Find integral 21 P=5 Sin (2x x3 x 10³ It dt- 3

A: To evaluate the following integral.P=5∫02πsin22π×3×103t dt

Q: dy cosx+ ysin x =1 dx

A:

Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: Find a differential operator that annihilates 4e2" cos 3x + 3x²e5.

A: Let L be the differential differential operator that annihilates 4e2xcos3x+3x2e5x. Find L.

Q: 1 dx 1) /x (1+ vx) 2) [ 2x* vx? + 1 dx x² + 1 dx

A: In the given question we have to calculate the integrals  (1)I=∫1x(1+x)2dx and (2) I=∫2x3x2+1dx we…

Q: 2. y" +4y= sin2x + x2 using inverse operator method

A:

Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

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Q: 3. f sin³y(2-3cosy)² dy

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Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: if Zcand Zp is complementary function Particular integral for the equation f(x X F(x,y) respectively…

A: This is Partial differential equation.