Q cschx= la Sinh! I

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

A:

Q: 14. S 5 sin 3x cos 3x dx 15. ſ tan? Ode

A: We can solve the given integral as follows:

Q: 2. Evaluate J dx (cos³x sin³x)

A:

Q: (d) y = sin(Vx) sinh (In x)

A:

Q: 28. Se cost sin 2t dt

A: ∫0πecostsin2tdtSolution :∫0πecostsin2tdt2∫0πecostsintcostdtlet, cost=x-sintdx=dxsintdx=-dxat…

Q: b,c,d

A:

Q: sin(2t)dt 0,

A:

Q: Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

A:

Q: L{sinh 6t– cosh t

A: we have to find the value of L{sinh(6t)-cosh(t)}

Q: Integrate cot(r) In(sin(x))dx.

A:

Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

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

A:

Q: 23. Lx? sin y dy dx

A: Given: ∫-11∫0πx2sinydydx for finding given integral we integrate one by one

Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: sinh(In In a)da is equal to xlnx

A: To find:∫sinhlnlnxxlnx dx

Q: 200 J + Corxiy_Tanx sinx dy

A:

Q: Find cosh² (t) sinh5 (t) dt.

A:

Q: Evaluate the integrals

A: We’ll answer the 15th question since we answer only one question at a time. Please submit a new…

Q: S sin Vat dt

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

Q: 3. Arctany dy

A:

Q: valuate the triple integral ***"* sin² (z)ze-²v³ dzdyda

A:

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

A:

Q: (A) Prove that: cosh x + sinh x = e*

A:

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: S tan ax secex dx 3

A:

Q: Find sinh + C sech V5 + C sinh () + C X. Cosh 5 O -1 csch--

A: Integral of the given function is -

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

A:

Q: If y- sinhx then prove that dy dx

A:

Q: I = f, (sinhz + 1)dz. %3D

A:

Q: eteR MiNe SiN IN°()COS)dx

A:

Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

A:

Q: cand. find dy at

A: Given that     If y=x2 - 4x and x=√(2t2+1) We have to find dy/dt at t=√2 .

Q: Jrin m In(cos m) dm

A:

Q: ind dy/dx if y= xsquared-cotx-1divided by x squared show all work

A:

Q: 2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

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Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: (g) sin vt dt.

A: Intigrating the given equation.

Q: vE zy sin{z° + y)dzdy Find

A:

Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

A:

Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

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: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: dy 1. sin 2ycos2y

A:

Q: dy 1+ sin 4y

A:

Q: er dy %3D sec da

A: The given differential equation is exdydx=sec y and the initial condition is y0=1. Solve the given…

Q: sin(20nnt) ass A: AS(t)ln:0dd En=1 %3D %3D1

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.