c) tan³ x sec³x dx 3

Q: classify and find genoral solution of differe equaton :- (l-2x² tany) dx– (x³sec^y ) dy=o

A:

Q: evaluate using Integration by Parts.

A:

Q: How to compute Cp using below equation, OP, sin 0; Cp, = 2 sin? 0; +2 cos 0 dy dy Where y = 0.5x…

A: To simplify: CPi=2sin2θi+2dθdyisinθi∫0yicosθdy

Q: dx 3 cos x+2 sin x-5

A: This integral can be solved by using the trigonometric formulas of sinx and cosx in terms of…

Q: 2-) Calcu late +he folloming integ rols by using the integration met hods a)| (hx" +8x²+ 15x) dx dx…

A: We are allow to solve one que at a time

Q: Using an appropriate substitution, the integral cosxe+2 sinx) dx is equal to:

A: Solve intregal

Q: cos z dz (4 + sin z)?

A: The solution of above integral is written in below steps.

Q: sec 2x da 4. I+3 tanzx

A: Integration methods help to find the answer to the problem. Substitution of the function helps to…

Q: aluate the integral. Зл/2 3|sin(x)| dx

A:

Q: Evaluate using Integration by Parts. -8x sin x dx + C

A:

Q: Using Variation of Parameters 4y''+4=cos-1x

A:

Q: sin(3 dx

A:

Q: (b) Use integration by part or tabular method to find i. 2e2" cos 3x dx. ii. x° sin 3x dx.

A:

Q: f (x, y) = sin(x + y?) near the point (7,0).

A:

Q: Evaluate the integral tan 4x dx tan? 4x - 24 nltan- O inltan 4x + Vtan? 4x – 24| + C 1 Arcsec tan 4x…

A:

Q: Find the total areas of the shaded regions

A: Required area is ∫-π03sinx1+cosx dx

Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

Q: (2) Separation of variable c. xcos?ydx + tanydy = 0

A:

Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A:

Q: evaluate using Integration by Parts.

A:

Q: d tanx = sec?x. dx Prove that sec² %3D

A: To prove the equation, we need to simplify the left hand side of the equation. According to the…

Q: Ly = Ce* + C2 cos x + C3 sinx

A:

Q: 7. fsins y cos' y dy

A:

Q: rcosA 2. r sin 0 dz dr de

A:

Q: 8 dx Evaluate | by trigonometric substitution integration method? (1+x*)²

A: You have posted multiple questions. As per the instruction, we will be answering only the first one.…

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

A:

Q: 4. sinx 1-sin² x dx

A: We have to find the value of the given integral ∫sinx1-sin2xdx

Q: rin 2 cosh x dx. Vsinh? r + 4 sinh r + 2

A:

Q: use a geoetry formula to find the exact value of the definite interval (-2x+4) dx on the interval…

A: The given function is (–2x+4) with the interval [0,3].

Q: 91. Prove the integration formula tanx dx = In | secx| + C (a) by using algebra and integration by…

A:

Q: Solve the equation using suggested substitution: (3siny-5x)dx + 2x2cotydy = 0; let z = siny

A:

Q: DIfferentiate y °x² - cas ķ sin x+ e vinx = 1 %3D DIfferentiate eln x3, find y!

A:

Q: sin x e" dx Cos x

A: To evaluate the given integral.

Q: Use integration tables to find or evaluate the integral ∫ 1 / sin   x cos   x dx

A: We have to evaluate the integral: ∫1sin x cos xdx We know the identity: sin2x+cos2x=1 Substituting…

Q: Calculate the integral (sec(x)+ tan(x))² dx.

A:

Q: check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the…

A:

Q: evaluate using Integration by Parts, substitution, or both if necessary.

A:

Q: In integrating the function f(3x + 5)(cos) dx using integration by parts, what would be your v? v =…

A: The integration by parts is done using the formula: ∫udv=uv-∫vdu. In general, the ILATE rule is used…

Q: sinx dx 5+ cor?x

A:

Q: ind general solution by separating the v y3 = (y* + 1) cos x %3D dx.

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

Q: I- USE THE INTEGRATION BU PARTS TO FIND : 1- lx -Jcx.cosX).dx 2-

A:

Q: Use trigonometric substitution to solve the integral Jx*V1+x² dx

A: Note the results :     (Identity)

Q: | sin? u cos udu

A: The given integral is: ∫sin2u  cos5u du

Q: Use trigonometric techniques of integration to evaluate tan12x sec x dx tan15x tan13x + C

A:

Q: The approximation of I = , tanx dx

A: The solution is

Q: Evaluate the integral tan 4x S- Vtan? 4x - 24 dx Arcsec sec 4x + C 5 1 Arcsec tan 4x +C V24 4/24…

A:

Q: (b) Evaluate the integral sec X dx J sec x- cosX

A: To evaluate the given integral

Q: Solve the fo llowing D.- E y + y tan X Cos X %3D

A:

Q: (x² sin(x')dx = 3 %3D

A: Given : Integration of X2sin(X3)dx

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.