-2y+2y=2e°cos(x

Q: 1 1. J dx x2 V9x²-81

A: Wr have to evaluate the integral.

Q: Question text Verify the Mean Value Theorem for the function f(x)=2x' + x? -4x-2 in [0.1]

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: (4x' - 6x) dx = 4x³ Evaluate

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Q: 1 dx csc³(5x)

A: This question is based on indefinite integral.

Q: -п/8 S sec? (2x)dx

A: We have to evaluate the definite integral: ∫0π8sec22xdx Assuming, t=2x Then definite limit will also…

Q: y = (r² + 4r) e"

A: given question is solved with the help of product rule of differentiation    i.e. (f.g)' = f*g'+…

Q: 1 I = J dx (1-x²)Z %3D 3

A: It is known that: 1-cos2x=sin2x∫sec2x=tan x+Ctansin-1x=x1-x212

Q: 1. L= V1 + 16x6 dx

A: First, we factor out 16 from the radical term, So, it becomes,

Q: d (x dx 미

A: ddxxx10

Q: 3 24- dx (3— 4x(х + 1)

A:

Q: olve the following: Each question is

A: Introduction: A differential equation is one that incorporates the by-product of an unknown…

Q: ysin2xdx-3y°cos?x dy -0

A: The given ODE is: y3sin(2x) dx - 3y2cos2(x) dy=0 This can be evaluated as follows:

Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

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Q: dy cosx + 3y = ,y(1) = 1.017 dx x2

A: Given that  The differential equation is

Q: Sezx(1 + e-2*)dx

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Q: 9. f 6 sec¹ xdx

A:

Q: Order One DE y'-(3tanx)y=1

A: The given differential equation is the linear of the form y' + P(x) y = Q(x) Where, P(x) = -3tanx…

Q: Simplify the expression xyz + x’y + x’y’

A: We have to simplify the expression xyz+x'y+x'y'.

Q: y = (In x)*

A:

Q: Find L'} se 's²+4'

A: In the given question we have to find the Laplace inverse transformation of the given function f(s)…

Q: 3 sinº x dx 4 Show that

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Q: √√x²+9 dx

A: Give integral is ∫x3x2+94dx

Q: dx 3 -1 (4-x²)7

A:

Q: Let y = xbex (where b is a real number). Determine y'.   Let y = (3x + 6)/(6x + 12). Determine y'.

A: given y=xbex to find the derivative y' use the product rule uv'=uv'+vu' therefore,…

Q: 35x dx ii. 321-x

A: Use the method of substitution to evaluate the limit. Let I=∫0135x3321−xdxAssume…

Q: 2. +x +1 d

A:

Q: Find the value of x'+7x-x+16, when x 1 + 2i.

A: