60 120 m%3D Equation %3D 1. 2.

Q: Score Lxi> 2

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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A: Given the integral ∫dxx24x4+932 We will use the the method of substitution to evaluate the integral.

Q: -8 dx

A:

Q: 3 dx x²+4x+29

A: Given,           ∫3x2+4x+29dx

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A: Explanation of the answer is as follows

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A:

Q: S- VE + 4) dx b)

A: We have to evaluate given integration ∫5x4-x5+4dx

Q: 2r +a*dx. 2.

A: Simpson's rule  ∫abfxdx=h3y0+yn+4y1+y3+--+2y2+y4+-- h=b-an, where nis multiple of 2. x1=x+h

Q: 30. G(x) %3D х3 -5e2х

A: Given  G(x)=x3-5e2x Now we have to find the difference of G(x) as shown below

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A: Fundamental theorem of calculus allows us to reduce computing the definite integral to computing a…

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A: The given integral is ∫09dxx-123 We have to solve the above integral

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A:

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A:

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A:

Q: 6. (x³ – 4x + 1)dx Solution:

A: As per guideline we have to solve only one question

Q: dx 6. S e2x+1

A:

Q: 213 dx 4+x² ,2

A: We will use substitution to solve the integral

Q: 28+メ+x dx 4x+16

A: Step:-1 Given that ∫1∞ 2x5 +x2 +x4x6 +16 dx Take  L = ∫1∞ 2x5 +x2 +x4x6 +16 dx L=∫1∞ 2x5 4 x6 +4 dx…

Q: Solve the equation  ye^(2x)dx = (4 + e^(2x))dy

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Q: Find the y' and y''. y= square root of 1- sec (t)

A: Consider the provided function, y=1-sect Find the first and second derivative of the function. Now,…

Q: [x³e'dx,

A:

Q: 7) | sec x. dx

A: Given:       ∫ sec5x dx

Q: +00 L e-y° dy = VTJ aw

A: In the question we have to prove the integration of given function.

Q: 7 е. 7g(x)dx = 5

A:

Q: dx= + C.

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Q: Evaluat dx (b) 2.6 m2

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Q: 3 dx x² +4x+29

A: Given that  ∫3x2+4x+29dx Using DI method, solve the given integral.

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A:

Q: Q3//A/ Evahuate 6. In(2)dx

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Q: 10 x) dx is

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Q: 1. (x+6у?)dx - 4хydy-0

A: Given problem:- (x2 + 6y2 ) dx -  4xydy = 0  Solve the given differential equation

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Q: Solve the D.E sec2x %3D

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Q: 10. S elog2 csc e* dx V1+tan²ex

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Q: 1 (a) dx, (22 – 8x + 15)i

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Q: d/dx (x2+1) lnx

A: Apply product rule to find the derivative (uv)’ = u’v + uv’

Q: 2x +1 (ii) Sa. dx . 6x² + x – 15 (ii) J

A: We first factor the denominator

Q: 7k +5)dx t

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Q: 15. dx 16x* - 1

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Q: (x* — 8х? + 10) dx %3D -3

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Q: 9. S 1 x√64+9x² =dx

A: The given integral,      ∫1x64+9x2dx

Q: et dx 3 (9 + e2ª)ž

A: Solution: ∫ex9+e2x32dx Apply u substitution: u=ex dudx=ex⇒du=exdx⇒dx=1exdu

Q: g(x) 9 arccos- 7

A: To calculate the derivative of the function g(x)=9arccos(x/7). Now, use the formula of derivative of…

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A: We have to solve

Q: .3 7. (x* – 8x² + 10) dx = Solution:

A:

Q: Figure 2: 4. x 54% 5. mLZ 5. Z- Y 6. mLY

A: