bn = s(t) sin(nw,t)dt %3D

Q: y = (sin x)e¯* find de sin-1y %3D d In x

A: y=sinxe-x. Then we have to find desin-1ydlnx.

Q: y = In (sin x) Find dy dx

A:

Q: 1?ei dt

A:

Q: sin(x²-1)y separable or not dy dx y2-1

A: To find given differential equation is separable or not .

Q: cos s x dx 2. S: Vsin x

A:

Q: Solve the integral equation y(t) cos t + y(x) cos(t – x)dx %3D

A: The given integral equation yt=cost+∫0tyxcost-xdx can be written as  yt=cost+ytcost Now apply the…

Q: t sin(2t)dt.

A: Given : ∫tsin2tdt

Q: Find dy/dx

A: The given expression is:

Q: sin(x) sin(y)dx + cos(x) cos(y)dy = 0, y (0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: 4th order RK method  yi+1=yi +16k1+2k2+2k3+k4Where ti+1=tn+h          k1=fti,yi,…

Q: OSx. ta- x dx OS cot J dxe OSx cot dx -1 S cos' 5ã dx Sx cos dax Ssec x dx O Se dx 10 PSos (dx) dx

A: Given: Given integrals are , 4.∫x tan-1x dx 5.∫cot-1x dx 6.∫xcot-1x dx 7.∫cos-1x dx 8.∫xcos-1x dx…

Q: PCx g) - Sin (zy)- Cosx'+x*y? %3D find d'f df dye' de dy

A: Given function is  f(x,y) = sin(x,y) - cosx^2 + x^2y^2

Q: dx 5. x- + ²x = sin t %3D dt

A:

Q: I 1 y sin(2²)dx dy. 0. y2

A: See the details solution in below

Q: dy - y cos x dx = y ln [yedk COS x]

A:

Q: Find I using integration or geometry: I = 5 dx dy .

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: *)CSフJつ dx 1/2 ウキ

A: Given integration is : ∫121sin-1xx3dx  To find the value of integration.

Q: dz %3D dt

A: Given that: z3=x3+y2, dxdt=2, dydt=1 and z>0.

Q: / sin(In |x|) cos(In |æ|) + dx COS -

A: We have to prove that the given integral is true.

Q: i y = tan-1(x)+ tan-1() dy + 10 dx

A:

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

A:

Q: sin(x) sin(y)dx + cos(x) cos(y)dy= 0, y(0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: We have to find y(1) using fourth-order RK.

Q: QI/ Find dx 少 for Iny=ex).csch"()

A:

Q: arsualuate the faltowmg integgal dx 4 Sin?x

A:

Q: sin(y) = -5x dy Also, dt 10. dx Find when y = -T. dt

A: Consider the following: Differentiating the function with respect to x on both sides, we have,

Q: d'y -+42=sin 2x 3 dx dx

A:

Q: dx? dx dt + 5- + 6x = 4t2, where x(0) = 0,x'(0) 0 dt

A: Second order intial value problem

Q: Solve for the differential of y when y= sinax, x=-, and dx= (A 4 B C) 4 D

A: Given; y=sinπx ,x=1/3, dx=1/2.

Q: Let y = tan(2x + 2). Find the differential dy when x = 4 and dx = 0.2 Find the differential dy when…

A: We have to find change in y

Q: y = tan(e*) + ey %3D

A: Given function is: y=tan ex+exy We have to find y'.

Q: xcos( x), sin(x) 8. dx = LHIN

A:

Q: a) | sin x dx Ssin'xe x+1 dx b) + 2x

A: We will use the double angle formula C=integrating constant

Q: еУ sinx dx 3Dcos*x dy

A: To Determine: we have a differential equation  Given: we have eysinxdx=cos2xdy Explanation: we have…

Q: dy -y In (yecos)dx 4. COS Y sin x dx

A: The detailed solution is given below Thank you

Q: L sin(t) dt

A:

Q: 25. dx is 1 (B) (©) ! (A) 2e (D) (E) divergent

A: see below the answer and calculation

Q: (g) sin vt dt.

A: Intigrating the given equation.

Q: Let y = tan(3x + 6). %3D Find the differential dy when x = 2 and dx = 0.3 Find the differential dy…

A:

Q: y = In (tan -1 (8x°)) dy dx II

A:

Q: ich option is an antiderivative of Sar 3x cos(-2x) dx a. 3 9.

A: We will use integration by parts to find the answer.

Q: (cos x2) dx. Use integration by parts. 1.

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Q: dx dx + e dr OI= +0 dx + 16

A:

Q: dx I [; (1-2x) I= [sin (4x) cos(4x)dx (In(x))3 dx I

A: Given

Q: Integrate the function. dx Jzx (1+x) A sin-1 +C tan-1 C In |x|•C D tan-1 .C

A:

Q: (v sin' 2) dn sin ædy

A: This is a question of exactness, non homogeneous differential equation.

Q: e* sec (e* +1)dx tanle* +1

A: We need to evaluate ∫ex sec2(ex+1) dxtan(ex+1)                              (1) Let tan(ex+1) = t On…

Q: Evaluate / e*cos(x)dx using integration by parts-

A:

Q: Using linear approximation, estimate e^0.1 cos(0.1)

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Q: dy TC * of y = In [tan (G +)1 dx

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Q: The integration A. 114 Β. π C. 0 D. 1/2 Z|7 sinc(4nt) dt has the value (hint:use the FT)

A: Given integral is ∫−∞∞sinc4πtdt. We have to evaluate the given integral. Here, ft=sinc4πt. Now, for…

Q: t sin (=) dt du

A: