INtegrate  sec2(2x+3)

Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: A non-exact equation can be converted to an exact equation by OA. Multiplying with the Integration…

A: Choose the correct option:

Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: Integrate: ∫sec^(3)2xdx

A:

Q: 9-x² dydx. 2

A: x = 0 r cos θ = 0 θ = π2 x = 322 r cos θ = 322 r = 322 sec θ   y = x r sin θ = r cos θ θ =…

Q: Q4. Find by implicit differentiation of 2x - 3y = 4

A:

Q: Describe the method used to integrate sin² x.

A: The process to find the integration of sin3x is to write in a way through which its differential can…

Q: 4. fx(1-x) dx

A: We can find the integration as below.

Q: 14. √ √2-√x dx

A:

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

A:

Q: Describe the method used to integrate sin3 x.

A: Given I = ∫sin3x dxTo integrate sin3x , substitute sin3x  = sinx . sin2xor sin3x = sinx . sin2x =…

Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" :

A:

Q: sech (x*) tanhl 12.

A: 12. Given integral is ∫sech3(x13) tan h(x13) x23dx Let us make substitution to simplify the above…

Q: integra 6. XVx - 8 dx Je

A:

Q: Verify the formulas by differentiation. ∫ sec2 (5x - 1) dx = 1/5 tan (5x - 1) + C

A: ∫sec25x-1 dx=15tan5x-1+C

Q: 3. у' %3D 2ху — х

A:

Q: f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

A:

Q: Solve the equation in the attached image:

A: Given:

Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" =

A:

Q: Verify the formulas by differentiation. ∫ (3x + 5)-2 dx = -(3x + 5)-1/3 + C

A: Given ∫(3x+5)-2dx=-(3x+5)-13+C Verify the formula by differentiation Consider Right hand side value…

Q: When do we use the method of substitution in integration? Provide an example.

A: Given- Substitution in integration. To explain- The method Substitution in integration. Concept…

Q: How is integration by substitution related to the Chain Rule?

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us…

Q: I need to integrate 1/(sqrt(a^2+x^2)). If I let t=x+sqrt(x^2+a^2) where t>0, then how do I…

A: The given integral is,

Q: Sec-S 2 1 TanOLO

A:

Q: 9. Differentiate y = /sec³ (5t2)

A:

Q: Integrate: dz V2x + 3

A: We have to find

Q: Solve by using gamma funcien. 2.2

A: We find value of Gamma (-2.2)

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

A:

Q: Integrate

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Q: у %3DIn(In sec x)

A:

Q: S sin4xVcos4x + 1dx

A: Let u=cos(4x)+1 Then du=(cos(4x)+1)′dx=−4sin(4x)dx  and we have that sin(4x)dx=−du4

Q: How do I calculate sec^-1 (1)?

A: Domain of sec-1(x) is (-∞,-1] ∪[1,∞) and Range is [0,π2) ∪(π2 ,π].

Q: evaluate the integral.

A:

Q: 1. y = Vt2 + 3t – 1 %3D

A:

Q: Solve 3x^2-Siny=0, xy^2-x^3+7=0, initial point (-1,2) .

A:

Q: Solve using partial differentiation

A: Given that  uxy=4eycos2x given that y = 0, ∂u∂y=cosx and u=y2…

Q: Integrate (tanx)^3(secx)^3

A:

Q: 1- Genx :1 CSCX 2 CSCX=1 senx CSCX = I CSCX = 2 %3D 2- Cotx = 3 tanx= 3J3 3. 3 tanx = Cotx 3. 13 353…

A: first one is wrong.because secx=1/cosx.and sinx=1/cosec x.

Q: (7 – siny)y' = 3x2 + 2x

A:

Q: Explain how successive over relation is obtained from the Gauss-Seidel method.

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Q: 2. f x cos² x dx

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Q: how do I integrate this

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Q: J7 -dz 21-8

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Q: sech2(In x)

A:

Q: When should I use partial integration and when should I use substitution?

A: When should I use partial integration and when should I use substitution.

Q: Vt3 e-st dt 4s2

A: Explanation of the answer is as follows

Q: Find the orthogonal trajectories of the functen X + ce-X which is . passing Thieugh (-2.0)

A: We need to find the orthogonal trajectories of the function y=x+ce-x, which is passing through (-2,…