dr =ズ Sin )=s OP Type a a exact awser Using X as needed

Q: tan'y - ycosx = sin? x + find y',y" If

A:

Q: 8. S sin x(2 – 3cos x)²dx

A: We have to evaluate the following integral.

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: Find y'. Given: y = -sin(4x)cot(4x) %3D

A:

Q: If sin v = with < v < T and cos w = * with 0 < w < , find sin (v + w)

A: Given that π2&lt;v&lt;π. So, v is in the 2nd quadrant.In 2nd quadrant sinv is positive but cosv is…

Q: d (cot x) show that – csq² x. dx

A:

Q: L[sin bd]- show that

A:

Q: Evaluate fe'(si Je*(sin x +cos x)dx

A:

Q: If rcos(x)sin(y)=a, rcos(x)cos(y)=b and rsin(x)=c, find r.

A: Formula used is written in the bracket of the first photo.

Q: rĩ sec² 0 (e) tan 0 do. Vtan 0

A: That's easy. Have a great day!!!

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

A:

Q: x3 V4 + x2 dx

A:

Q: Apply Newton’s approx. to find the value of x for cos x = sin x; x0 = 1.

A: Topic-  Numerical Analysis. Newton's approximation Formula: xn+1 = xn - f ( xn)f' (xn)

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

A:

Q: sin 4y w = y+1

A:

Q: Differentiate y = In ( sin² (4x)). A y' = 8 tan (4x) y' = 8 cot (4x) y' = 8 csc2 (4x) sin (8x) y' =…

A:

Q: Q/ ind dy if 24-sini' (xe!)=sin'(x*)+ cos (x")

A: Given that      2y - sin-1(x2+1) = sin2(x4) + cos2(x4) Here we have to find dy/dx.

Q: Compute / / sin(x²) !! dr dy.

A: The double integrals can be solved by solving the inner integral first followed by the outer…

Q: (i) | sin' xcos xdx .

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Explain why trigonometric substitution eannot be used where x = 2 sin 0 on dx 4 – x2

A: We have to calculate the indefinite integral

Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

Q: coth*(sin 3z) 12) zp- V1- ? 3z tanh

A: Integration of given function

Q: Prove d [sin-! lu(x))]= I dx dulx) %3D NI- Culx)]? dx

A:

Q: Evaluate: cot[ sin! V212] O 2. O VZ 12

A:

Q: tanla= 2 with 3T LaL2p 3 2 and Sin lb) = 3 with IT L6LT 2. %3D

A: Solution:-  tana=-23   with 3π2&lt;a&lt;2π (fourth quadrant) sinb=34 with    π2&lt;b&lt;π   (second…

Q: tim Sin It tanx\

A: We will find this limit by substitution

Q: coth“ (sin 3z) -dz /1– tanh² 3z 12)

A:

Q: General Sol. of  y' tanxsin2y= sin2x+sin2y is

A:

Q: What is the antiderivative of -tan(x) + pi^x?

A:

Q: sečxdx ztanx 5-9tarix ansi sin 2

A: Solution is done in step 2

Q: We wish to compute sin° x cos“x dx,

A:

Q: What is the antiderivative of sin^2(x) + 2sin(x)?

A: Antiderivative of sin^2(x) + 2sin(x) is given by,  ∫[ sin2x + 2sinx ]dx =∫sin2x dx + ∫2sinx dx

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

A:

Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

Q: 6. Se¯*tane¯*sec?e¬*dx

A: To evaluate: I=∫e-xtan(e-x) sec2(e-x) dx=∫tan(e-x) sec2(e-x) (e-x)dx...(1)

Q: evaluate using the appropriate method or combination of methods.

A:

Q: Integrate e^(2theta)*sin(3theta)

A:

Q: Show that: cos hz = cos hx cos y + i sin hx sin y.

A:

Q: coth“(sin 3z) 12) Vi- dz /1– tanh² 3z

A: The given integral: This can be written as, To evaluate the integral:

Q: If x is measured in degrees and f(x) = cosx, then d f(x) = − sinx

A: To write that it is true or not.

Q: Is this: sin x cos y- cos x sin y/ cos x sin y reciprocal quotient pythagoreom  algebra

A:

Q: Show that tan(arccosx) for |x| s 1, x + 0.

A:

Q: Evaluate sin (x) e-x dx by use Simpson's rule. h=0.5

A:

Q: Cos x [SND] If y = tan x+ seç show that, y = (1 – sin æ)?

A: Topic  =trigonometry

Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

A:

Q: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2&gt;0 then…

Q: Sirzy-L652X こつinてy Cos? x CoSz seczK-

A: As per guideline we have to solve the 1st one. For another solution request again

Q: (11). - cos?(2y) sin? (x), y(등) =0 Workings y= tan '(z - 글sin 2v) +

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.