Evaluate the integral by making the substitution u = x – 6.

Q: Evaluate the integral by making the given substitution. Sx x +2 dx, u = x³ +2

A: The given integrand is  x2 (x3+2)1/2

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: Taking substitution

Q: g+y= 쓸 - zxe - 5

A:

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A:

Q: 4 dx, u= 1 + 2x (1 + 2x)

A: Explanation: Given that: ∫41+2x3dx,      u=1+2x Concept: 1. ∫xndx=1n+1xn+1+C Calculation: First…

Q: Evaluate the integral by making the given substitution dx, u = x³ -6 -6

A:

Q: x In(2 + x³) dx

A: Topic  = Integration

Q: Evaluate the given integral with suitable substitution : 5z 10r (20 + 20) dr

A: Explanation of the solution is given below...

Q: Evaluate the integral by making the given substitution. dx u = 7x + 8 (7x + 8) '

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Q: de V1+4x

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A:

Q: Evaluate the integral f xe6x dx

A: Given :          ∫xe6x2 dx   To evaluate the given integral.

Q: c/4- 4 – x dx

A:

Q: 20. J 1 (x+25)√√x dx

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Q: Evaluate the integral by making the given substitution. [sec (3x)tan (3x)da, u = 3x +C

A:

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A:

Q: Evaluate the integral by making the given substitution. x-Vx3 + 10 dx, u = x3 + 10

A:

Q: Use the substitution x 5 sec t to evaluate the integral dr x/x²–25

A: We have to evaluate the integral ∫dxxx2-25 by substitution x=5sect.

Q: Which integral could be evaluated using the substitution u = x ?

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A:

Q: Evaluate the integral by making the given substitution. dx u = 7x + 4 (7x + 4)3 + C

A:

Q: 2. dx 1+√√x

A: integration

Q: Evaluate the integral by making the given substitution.   ∫ x2  √( x3  + 1)    dx , u =  x3   +1

A: The integral formula to be used are: ∫xn dx=xn+1n+1+C, where C is an integral constant. The integral…

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the improper integral xe d

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Q: Evaluate the integral using an appropriate substitution. dx = +C x√√8-xd

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Q: 5. -dx 1 + x

A:

Q: Evaluate the integral: / In(r")) d.x.

A: Solved below

Q: Evaluate the integral (= - 11)" de, 26 by making the appropriate substitution: u = 26 |- NOTE: Your…

A: Proceed as shown below...

Q: Evaluate the integral of the following using Miscellaneous Substitution 3. x /x*+ 1dx

A:

Q: Evaluate the integral by making the given substitution. dx u = 3x + 9 (3x + 9)3 + C

A:

Q: Evaluate the integral by making the given substitution. x³(10 + x*)7 dx, u = 10 + x4

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Q: use substitution to evaluate the integral in terms of f (x).

A:

Q: Evaluate the given integral with suitable substitution : (36z + 36) dr

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Q: Evaluate the integral by making the given substitution. xV+ 14 dx + 14 dx, u = x3 + 14

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Q: Evaluate the integral using an appropriate method. J = 3 22+5+6 dx

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the integral of the following using Miscellaneous Substitution dx 1+ X

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Q: I = 2т dxdydz Is

A:

Q: Evaluate the integral by making the given substitution. dx (3x + 14)4 u = 3x + 14

A: We have to solve

Q: Evaluate the integral m(x) dx x2

A:

Q: Evaluate the integral J*(x*-1)°dx by using substitution.

A:

Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

A:

Q: dx

A: Let  x-2 = t  Differentiating both sides dx= dt

Q: Compute the integral by algebraic substitution: ∫7/2+√x-4 dx

A: We need to compute the integral ∫72+x-4 dx Now, using the property ∫a fx+bgx dx=a∫ fx dx+b∫gx dx…

Q: ここXP x(メャッ)。

A: put x^2+7=u so that 2x dx=du .and solve the question in 2nd step.

Q: Evaluate the integral by making an appropriate u-substitution an applying any necessary formula(s).…

A:

Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral below. V3x +2 dx

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Q: /1- xº V1-x°

A:

Q: Evaluate the integral J 1 dx 9+x2

A: Given,             ∫19+x2dx

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.