If y = tan u, u = v - and v = In x, what is the value of y at x = e? dx sec? e 1 O Option 4 O Option 3 2 O Option 2 O Option 1

Q: 1. tan? x dx 2. | cot2 x dx

A: 1.∫tan2x dx2.∫cot2x dx

Q: sec² 0 de tan² 0 – 1

A: Integrate the integral.

Q: 4. Which is negative, 8 dx or 8 dx?

A: We find the integrals first

Q: sec(/æ) tan(/x) dx

A:

Q: 9. 4 sec2 0 tan 0 d0 0,

A: The solution is given below

Q: Evaluate without using a calcu lator (tw" () CoS (tan"

A:

Q: S sin? x dx

A: ∫sin2xdxUse the identitysin2x=1-cos(2x)2∫sin2xdx=∫1-cos(2x)2dx                 =12(∫1dx-∫cos(2x)dx)

Q: is If У%3D2х arccos x - 2/1-х? then dx

A: We differentiate both sides with respect to x and then solve it.

Q: Use substitution to evaluate dx.

A:

Q: 1. S(1+ tanx)?dx

A:

Q: ex dx 25. - ex+1

A: ∫exdxex+1

Q: dy If y = vu² + 1 ; u =+x?, find dx

A: Derivative of the function

Q: 3. Evaluate dx. Hence find the value of sinx dx. Va -x)

A:

Q: y" "yi g= coshox + sinhɔxi

A:

Q: S sins dx cosx 2.

A:

Q: S5x sec?x dx 5.

A:

Q: [ sin (inx)]

A: (1).  We have to find: ddxsin2(ln x)

Q: Evalu

A: Given, I=∫-12∫z2z∫0ydx dy dz To Find: Value of I

Q: S cot-1 2x dx

A:

Q: viry? y Sinx dz dy dx

A: We need to evaluate ∫0π∫01∫01-y2y sinx dz dy dx = ∫0π∫01y sinx∫01-y2dz dy dx= ∫0π∫01 y sinx z01-y2…

Q: 14. Evaluate cos 3x+ dx. 2

A:

Q: Solve the diffgerential Eauation by Separating the Vaciables ex dy 2x %3D

A:

Q: Sx.Sinx Cosx.dx

A:

Q: If y dy then dx y = 4x

A:

Q: 8. S cot?x dx

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

Q: Sa sec ede tan' 0+9 tan e

A:

Q: 80 jess X e-x sin x dx.

A:

Q: Find Dxy. y = x6 - csc x + 4 O 6x - csc x cot x O 6x5 6x5 + csc x cot x O x5 - cot?x + 4 O 6x5 +…

A: