d In (t2 + 1) dt = dx A) In(x6 + 1) B 3a In (a? + 1) 3x ln (a6 + 1) In (x® + 1) In (e? D -

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

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Q: 3. (a) Compute ,12x – 1| dx in two ways. i. By using properties of the definite integral and the…

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Q: d Vi In(t)dt equals dx

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Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

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Q: Solve D.E using Exact from first order 2.xy dx +(x² +3y²)dy

A: To solve the given differential equation.

Q: x² + x - 1 dx J, x(x2 – 1) is convergent or divergent.

A: We have to solve the integral and check it is convergent or not

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Q: Consider the PVI with a second-order ODE, linear, with constant and inhomogeneous coefficients,…

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Q: 5e3* dx 9-12e3* + 4e6x ,3x 6.

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Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A: The Leibnitz rule for differentiation under integral sign is,…

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Q: d Q. * VE In(t)dt equals dx a. 4x³ (ln x) – 2 In(2) b. 4x³ (In x) – v2 ln(2) c.4x° (In x) d. 16x°…

A: Using leibniz integral rule -…

Q: 1. Evaluate the ff. integral f, (5x6 + 3x³ + 6)dx ·1

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Q: Q4\ Use Laplace transform to solve differential equation in figure below: dx + 3x = e dt -2t subject…

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Q: 1) Find dy/dt for if : y = log2 (8r'n 2) %3D 2) Evaluate the following integral: In 2 ` log2 (x +…

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Q: d Q. S Vt In(t)dt equals dx a. 4x³ (In x) – /2 ln(2) b. 4x5 (ln x) – /2 ln(2) c.4x³ (ln x) d. 16x°…

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Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

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Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: 1. Find the total differential dw. 2. w = re2u +e-V

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

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Q: . The exact differential d(xy)= xdy + ydx, what is the d( = 4x²y'dy+2xy*dx.

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Q: .2 -dædy In (x) ey

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Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: (a) Evalate the integral||xydy dx. 12

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Q: Use the Beta and gamma function -1 n! 1- Prove that x™(ln x)"dx (m+1)n+1

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: d ca+ Q. dx * Vt In(t)dt equals a. 4x° (ln x) – V2 In(2) b. 4x³ (ln x) – V2 In(2) c.4x³ (In x) d.…

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Q: Consider a delayed logistic equation of the form z(t + At) = z(t) + ar(t) (1– z(t – 2At)' K (a)…

A: Given: Let us consider the given delayed logistic equation of the form, xt+∆t=xt+αxt1-xt-2∆tK and…

Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: Solve the integral: dy dx. x2 H/4

A: To solve: The integral ∫141∫x2xxydydx. Formula used: ∫xndx=xn+1n+1+C Here, C is constant of…

Q: (b) Use the total differential dz to approximate Az. dz = X

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

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Q: d*y dr -y = 8(x – a); dx4

A: Differential equation is an equation that represents the relation between variable and their…

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A: Find the integral using substitution method

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A: Given,          ∫3x25+x2dx

Q: 1. Evaluate the integral 2 dx x2 +4x + 20

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Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: (a) Evaluate the integral [x (x* -1) ´dx by using substitution.

A: To evaluate the given integral ∫x3x4-12 dx by using substitution.

Q: Find the integrating factor: dy 3y = x (1 + x?) dx e3x None of these e-3x x3

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Q: 4) Evalvate the integral E 4 1+x² dx

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Q: 4. Express the integral e-t tổ dt in terms of gamma function.

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Q: d If g(x) == _S^*[e' − In(2t+1)]dt, find g ''(x) . - dx -2 2 A (2x + 1)² 4 B (2x + 1)² 4 (2x+1)2…

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

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Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

A: