Show that (i) | te 3 sint dt 50 -3t %3D

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

Q: =D{sinh(2r) – ţa dy/dx agi

A: We know that sinhx' = coshxx' = 1 and (f(g(x))' = f'(g(x))g'(x)

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: Can i get help step by step please

A:

Q: Find

A:

Q: I = | In(ax + 1) dx, for a > 0

A: Find the integration of I

Q: d²y nd by implicit differentiation if 3x² – 7y? = 14. dx?

A:

Q: Solve J. e-t sint dt. 0,

A: Introduction: The Laplace transformation is very useful in determining the integral. The Laplace…

Q: Q3. Evaluate : IL (2) * dy dx

A:

Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

A:

Q: The 2nd derivative of y = 24r is A 2*+2 In(8) B 2tr+4 In(4) © 24r+4 In(2)

A: Given that: y=24x

Q: SOLVE THE FIRST ORDER DE. dy – yln(yecosx)dx = y sinx dx

A: dy-yln(yecosx)dx=ysinxdx

Q: Solve for the following implicit derivative: d²y si sen(y) = ycos(2x) dx?

A: We have to find the double derivative of the given function.

Q: f (t) sinh 3t + cosh 3t 2t3 -

A:

Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: (solve exact de) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xye )dy

A:

Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

A:

Q: J (secs x) dx/csc x

A:

Q: Evaluate the derivative of the function. y%3Dsec(6 In 8x) -1(6 In 8x) dy %D dx

A: The objective is to find the derivative of given function

Q: Find cosh² (t) sinh5 (t) dt.

A:

Q: d Use the Fundamental Theorem of Calculus to find the derivative. dx dt 1+ vE

A:

Q: (2х — Зу)dx + (2у — Зx)dy %3D 0

A:

Q: Find dy Ser ysX"+3*+ e° dx + sin (1nx)

A: Given that: y=xy+3x+ecos-1x+sinlnx

Q: S sin Vat dt

A: Let the given integral be: I=∫sinat dt

Q: Evaluate the derivative of mq4.4.png cosh (bVx3 f(x) = a ln sinh(cx2) if a = 69, b = 0.6, and c = 6…

A: Given function: fx=alncoshbx3sinhcx2 To find: The derivative of the function f'(7) using…

Q: Solve: dy + y² = ty dt

A: A differential equation is said to be Bernoulli's equation if the equation is of the form…

Q: V3x d. Evaluate dx sin(3t) dt

A:

Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: Find the derivative. X dt 14) dx lol 0 5t+ 6

A: To find the derivative of given integral.

Q: hat is the number equal to L sin (3rt) dt?

A:

Q: tan st e dt 2

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: In the integration What is the implicit derivative of u? V9-4x* a. du = 2dx b. du = * c. du =– 2dx…

A: Implicit differentiation of integral

Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: Solve drc dt dy dt 200 +

A:

Q: 3.1.1 L sinh 3t dt

A: The Laplace transform can be obtained using the table of the transforms. The integral for the…

Q: To use differentials to approximate V8. You would use x = and dx

A:

Q: 5. f (t) sinh 3t + cosh 3t – 2t³

A:

Q: Find dy/dx implicitly. exy + x2 - y? = 11 |

A:

Q: calculate the derivative.

A:

Q: find the antiderivative of dx/sqrt(ex-1)

A: To find : The antiderivative of dxex-1 Solution The antiderivative can be evaluated as, ∫dxex-1 Put…

Q: Calculate cln 2 I = Ver – 1 dx thanks to the change of variable u Ver – 1. U = -

A:

Q: Sind dy forys(x) dx 3517X

A: y=(xx)3sin x

Q: 2. Solve the ODE using Separation of Variables. dy dx 5x²+4 y+1

A:

Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

A:

Q: Find (dy)/(dx) if ey = ex + sin(x2x).

A: Given ey=ex+sinx2x

Q: Let x > 0 and b > 0. Show that

A:

Q: 9. 2y(у? — х)dy — dx, when x %3D2,у %3D 2

A: Given that: 9.     2y(y2-x)dy=dx,    when x=2, y=2     NOTE: As per our answering guidelines, we can…

Q: If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the…

A: We have given,