zyć dziedzinę naturalną funkcji f (x) = log (arc + arc cos log, (r- 1) + 2 are sin %3D r+4

Q: tan + x Anctan ly =0

A: The given differential equation is,

Q: IT Evaluate the integral: (cos x + sinx cosx)dx

A:

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

A:

Q: sec?x Integral tanx

A:

Q: The trigonometric integral fs sec² x (tan³ x - 2 tan7 x) dx is equal to

A:

Q: Evaluate the definite integral.

A:

Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

A:

Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: to tal differential of eind the the り23 function ] 2=e + tan Z= Sin 2.

A:

Q: Integration of (Sin(x) + Cos(x))e^x is_

A:

Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

A:

Q: Evaluate the Trigonometric Integral sin (x) cos /2 (x) dæ ,3) sin° (x) cos

A:

Q: indefinite integral* ((sin^−1 (t))^2) dt

A:

Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: sin a cos x tan2 x dy find using Given that y = da logarithmic differentiation.

A: Given,       y=sinx cos4x tan2xx5

Q: y = cos (arcsin væ) + sin ( arccos 2

A:

Q: Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

A: The solution of the problem is given in the next step.

Q: Integral sin( +6)dt

A:

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: Verify Rolle's theorem for the function sin x f(x) = et on [0, n]. %3D

A: Given:                      f(x)=sinxex on 0,π                     f(x)=e-xsinx     The mean value…

Q: | cos (nt)sin(at) dt Find

A: This integral can be solved by the method of substitution.

Q: Evaluate sin(x) · In ( cos(x)) dx using integration by parts.

A:

Q: siny dle = (1-x cosy) Cas y

A:

Q: Use Simpson's rule with n = 4 to approximate cos(r) -dx Keep at least 2 decimal places accuracy in…

A:

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Use the Fundamental Theorem to evaluate the definite integral exactly. 16 Enter the exact answer. 16…

A: Given query is to find the value of the integral.

Q: Find Fourier transfarm f x #1= cos aut ut

A: Given the x(t)

Q: integral of (e^2x)(sin3x) using u=e^2x

A: Given, ∫e2xsin3xdx    We have to find the integral

Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

A:

Q: ( 3cos³x-1 To evaluate the integrand can be transformed to 1- sin?x O [(3cosx - sec?x)dx o f3cosx (1…

A:

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: Verify Rolle's theorem for: f(x) = e*(sinx - cosx) on

A: Given:

Q: Consider sin °x cos2x dx. f we let 4=cos x, the integrand can be transformed to

A:

Q: sin 3x dr + 2y cos* 3x dy = 0 COS

A:

Q: Quiz, Qi Prove that the arc lenfth of Curve to y = log secx from N =0

A: Given : The curve y = log sec x.   To prove that the arc length of the given curve is

Q: Find Fourier sertes [o, 2] an 2) fex) f Cx) = Sin X ニ

A:

Q: Differentiate y= arctan sinh x. coshx A. 1-sinh x cosh x B. cosh x C. ainh-x D. 1+sinh-x

A:

Q: Determine the following indefinite integral. Check your work by differentiation.

A: To evaluate the integral: ∫16cos2w-81sin2w4cosw-9sinwdw Solution: We know that…

Q: let h (z) =(arcsin(5z)+ln(4-z))^27. find h'(z)

A:

Q: Evaluate the integral sin dt. sin dt%3D

A:

Q: do sin 0 – cos 0 cos 0

A: The given integral is ∫dθsinθ-cosθ

Q: Differentiate: arctan(cosh(x)) Show all working out.

A: to find the derivative of arctan(cosh(x)) proceed as follows we know that ddxtanx=11+x2  apply chain…

Q: Module 7: Participation Activity #6 Calculate the derivative d In (t)dt dx using Part 2 of the…

A: Let the given derivative is,

Q: Evaluate using Cauchy's Integral Theory: OP 3+ 2 cos (0) + sin (0)

A:

Q: Find the integration of the function given using Transformation by Trigonometric Functions. S sin*x…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…