%3D f(z) Let h(x) = J) where f(x) = In(x+1) and g(x) = 4x + 2. What is h' (0)?

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: Using S- dx x√√x-1 Rationalizing Sfy)dy, find ffy)dy Substitution

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Q: y)dx

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Q: cosh x dy + (sinh x)y = e-* dx

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Q: sin(x²-1)y separable or not dy dx y2-1

A: To find given differential equation is separable or not .

Q: dy 1- Find by implicit differentiation. dx 2- x2 + y2 = 100. 3- x3 + y3 = 3xy². 4- x²y + 3xy3 – x =…

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Q: S2x²e** ax=uv- Jvau -Svau. Sfoxe". Using Integration By Parts, Find uv- Jv du- 3 x² e dx O 2 x3 x3…

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Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

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Q: B)ls w = z²1² analytical function or not?

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Q: dy - år if y = In (sinh 50) and x = cosh 40 dx

A: Solving the problem by doing the derivative.

Q: x2 dy dx by reversing the order of integration. 4/x 1. Evaluate

A: Given double integral is∫14 ∫4x4x2 dy dxNow , By interchanging the integral we have ,∫y=14…

Q: integral (dx/(√(x)+x))

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Q: 2- X %3D +2 3- Coshx dy +(y sinh x+e) dxo 36

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Q: Q6. Using Rule l-IV to find an integrating factors. (x² + y² + x)dx + xydy = 0.

A: Given- x2+y2+xdx+xydy=0 To Find- The integrating factor of the above differential equation.

Q: What is / - z dx? 1-x² o f- dx = -2cos-lx + C V1-x2 S- dx = 2sin-lx + C (1–x2 S-d 2 dx = 2cos-x + C…

A: 1. I=∫-21-x2dx =-2∫11-x2dx =-2sin-1x+C    ∵As ddx(sin-1x+C)=11-x2⇒∫11-x2dx=sin-1x+C=-cos-1x+C…

Q: Find dy/dx by implicit differentiation. x2 + xy - y2 = 4

A: Given function is, x2+xy-y2=4.   It is implicit differentiated as follows:…

Q: x +1 -dx x² (x – 1) (a) Integrate

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Q: e dx (1) S. 1-e2x (integration by substiution)

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Q: Find the differential dy when x = 2 and dx = 0.1 Find the differential dy when x = 2 and dæ = 0.2

A: ddxtanx =sec2x ddxxn=nxn-1

Q: 8. dx +x2 Integrate:

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Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: dy - cosh x dx + (sinh x)y = e¬x

A: see the details solution in below

Q: (a) Find the derivative. = In(x) – In(x - 8) dy dx (b) Find the derivative. y = In X - 8 dy dx %3D

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Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

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Q: Using separation Variable. 1.) In x dx/dy = 2 / xy^3

A: Given differential equation lnxdxdy=2xy3

Q: dx 62 + x² Integrate:

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Q: find the integrating factor of (y² - x ) dx + 2ydy = 0

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Q: dy cosh x dx + y sinh x = 2 cosh x sinh x

A: We will find out the required general solution.

Q: Integrate dx/(x+1)(x^2+16) from 0 to 1

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Q: Integrate f dx using integration by parts. x+1

A: Please refer the attached image for complete solution.

Q: y= sinh-lx then prove that Vx2+1 dx

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Q: Q1: Find the Integration using Gamma Function Method: x*e-3xdx 0.

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Q: g. cOS x Vsin x dx

A: Let sinx = t

Q: Find dy/dx by implicit differentiation. x7 + y4 = 5

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Q: Find dy/dx by implicit differentiation. 2) x3 - 2y2 = 1 4y B) x2 + 1 A) 4y C) 2y D) x2

A: solve the following

Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

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Q: Solve using separation of variables xy^2 dx + e^x dy = 0; when x -> infinite, y -> 1/2.

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Q: Uniclaretiana Fundoción universitaria Claretiana 1 (In x - 4) dx – (x + 1) dy = 0 2 4 +6x) dx +…

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Q: 9. S sec 2x dx 10. S cos x esin x dx 11. dx x+1

A: Evaluation of the above integration is

Q: (2xsinycosy - x+2x²evx´ )dy =(y-sin?y -4xyex )dx

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Q: A. Integration By Parts 1. ſx5Vx3 + 1 dx 2. S/* x sin 2x dx 3. S- x³ex? -dx (x2+1)2

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Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

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Q: related rates - find dx/dt where x2 +xy - y2 = 20. dy/dt = 5 and x = 4

A: x2 +xy - y2 = 20Diferentiate both sides with resepct to t. While differentiating recall the:Chain…

Q: 1 B3. Evaluate dx, using substitution method.

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Q: In x Find y' if y = e3 1 – 4 In x Based on your work from (a), evaluate - dx. -5

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Q: (B): Find the integration by using substitution method √x√2x-1 dx

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Q: Find the relative extrema of f(x) = (x − 1) cosh x − sinh x.

A: Maxima and minima: f(x)=(x-1)coshx-sinhx f'(x)=(x-1)sinhx+coshx-coshx f'(x)=(x-1)sinhx…

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;

Q: | (In x)2 dx Use integration by parts.

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.