y = tan(e*) + ey %3D

Q: 2. S V3+ Vã dx

A: Given: I=∫3+x33dx   ...1 Apply the substitution method to solve the given integral. Let,…

Q: 1. dx (x - 2)3 EXOX

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Q: Integrate the function. 2 – 25 dx

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Q: Evaluate [(e²/² - x)(e²/² + x) dx. Show your work.

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Q: How did you found x and dx? I 'm lost in that part

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Q: How do you multiply

A: Given radical expression is,

Q: +e Differentiate y = eX - e -x

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Q: iii. Sx coth-x dx.

A: (III) Apply the integral by parts rule, ∫u.vdx=u∫vdx-∫dudx.∫vdxdx Here, u = x and v=coth-1(x) As we…

Q: intergral x^e^3x^2+1 dx

A: I=∫xe3x2+1dx Then let I1=∫xe3x2dx, I2=∫1.dx Then, I2=x Let fx=xe3x2

Q: tunx dx

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Q: integrate e^x + e^-X/ (e^X- e^-x)^2 dx

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Q: integrate: [e^(2x)]cbrt(e^x +2)  dx

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Q: +e Differentiate y x- e -e

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Q: 25. х* dx dy

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Q: Q2 _Calculate the integration (a) |(5x2 – 8x + 5)dx

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Q: de (iv) x(y² – 1) + y(x² + 1) dx

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Q: - 1 dx

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

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Q: coshx 1. S –dx 2+3sinhx

A: "Since you have posted a question with  multiple subparts, we will solve first question for you. To…

Q: dx x lnx√9 ln²x-1 S

A: Given: I=∫dxxlnx9ln2x-1   ...(1)   As we know that; ∫1x2+1dx=tan-1x+C

Q: dx is approximately

A: The midpoint rule uses the midpoints of a subinterval:

Q: x3 e2x dx. Integrate

A: ∫12x3e2xdxThis can be done by two steps;Step-1:integrate without limitwe can integrate by parts∫fg'…

Q: 10. S Sec®(x) csc(x)

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Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: 4. cscó 3x dx 5. ſ cots x dx

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Q: eral solution. - 1) dx + (3x – 2y + 3) dy

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Q: dx S- x4 - 1

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Q: 3) Se-*.cosh(2x) dx

A: cosine hyperbolic function we can write in terms of exponential function Coshx= [e^(x)+ e^(-x)]/2

Q: [x7'dx Integrate:

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Q: Integrate: x dx (xt1)(x*+2)

A: Given data: The given integral is I=∫x2(x+1)(x2+1)dx. The given integral can be written as,…

Q: nS ISIna X -

A: Consider the quadratic equation as x2 – 12x +24 = 0.The formula for the general quadratic equation…

Q: cosh x dx е e- 2х

A: Given integral is ∫coshxe-2xdx

Q: Use the Product Rule to calculate e2*. dx

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Q: + xln\ V 1 – x° | dx

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Q: 4. S V4x –1 dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: S(4 csc" x-1)dx х-

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Q: 10 ii) J1 x(10+lnx)3 dx

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Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

Q: Ln3 2X dy dv

A: Part i,Given,          ∫0ln3ex1+ex12dx

Q: 2 dx X + X - e メ-

A:

Q: Differentiate y = e9 tan E

A: y=e9tanxy'=e9tanxddx(9tanx) [chain rule]y'=e9tanx×9ddx(tanx)y'=9e9tanx·sec2xddx(x) [chain…

Q: Vx(4- x)dx 2x e - 1 ,2x +1 e

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Q: Va(ln(x))² dx

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 3. dx V3-x

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Q: dy Flnd - of x³+y³=6xy dx

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Q: 3. dx 6X dx VT-x2 1-x² Et2

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Q: 5 |V25 – x² dx Compute the value of

A: Given: I=∫0525-x2dx we know that ∫a2-x2dx=x2a2-x2+a22sin-1xa+c                                  ...1

Q: 2) dx 4. - |

A: We can use method of substitution in order to solve the problem problem.

Q: 4x V x4 + 13 dx =,

A: Given: ∫4x3x4+13dx

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.