Evaluate the integral x(x – 5)7/2 dx by making the substitution u = x – 5.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A:

Q: Evaluating the integral f In(r³)dx, where x > 0 yields:

A:

Q: dx 6. Evaluate the improper integral. x² +3x+ 2

A:

Q: Evaluate the integral dx (5ӕ + 10)2 by making the appropriate substitution: u = dx (5x + 10)? II

A:

Q: +00 dx -Evaluate the improper integral x (In x)²

A:

Q: Evaluate the integral. dx a > 0 (a² + x²j3/2?

A:

Q: Evaluate the integral. (Use C for the constant of integration.) Зx In(x) dx ,2 -36

A:

Q: Evaluate the integral. (Use C for the constant of integration.) S. x² – 16 dx x3

A:

Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

A: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

Q: Evaluate the integral. -^x dx e S² sin √1-x² 2

A:

Q: evaluate the integral.

A: then integrate by substitution

Q: dx 7. S x V9x2-1

A:

Q: Evaluate the integral VI- 1 /1 dy dx. – x² – y2

A:

Q: Evaluate the following Improper integral: dx , x² + 2x + 4

A:

Q: Q5. Evaluate the improper integral dx x(Inx)7

A:

Q: Evaluate the indefinite integral. x2 + C dx J (x²-7)5/2 x(² –7)

A:

Q: Evaluate the integral.

A: Given integral: ∫121241-x2dx

Q: +00 dx II. Evaluate the improper integral x(In x)²

A:

Q: x-3 dx r³+9x +9.x

A:

Q: Evaluate the improper integral 2x dx, if it exists. (x² + 81)² 8.

A: The value of the integral ∫-∞02xdxx2+812 is given by: ∫-∞02xdxx2+812=-1x2+81-∞0=-181-1-∞=-181-0=-181

Q: Use symmetry to evaluate the following integral. | (6- |x)) dx - 1

A: The given integral,     ∫-116-xdx

Q: Evaluate the integral f e² In (x²+1)dx

A: ∫e2ln(x2+1)dx

Q: Compute the integral 1 dx. L (* – i)(x² + 1)

A:

Q: Use substitution to find the indefinite integral

A: Given ∫1xlnxdx

Q: e*dx e2x +1

A: We know that; ∫axdx=axlna+C And ddxcot-1x=-11+x2   Given: I=∫7cot-1exexdxe2x+1   ....1

Q: Evaluate the integral x3 dx 2+100 S x3 dx +100 (Use C as the arbitrary constant.)

A: Given,

Q: Find the integral of dx V1 – x²

A: Solve by integration

Q: Use reduction formula to evaluate the given integral xe" dx

A:

Q: evaluate the integral.

A:

Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: тх e COs nx dx

A: We have to evaluate the integral  ∫emx cos nx dx.

Q: Evaluate the integral dx (2a + 6) by making the appropriate substitution: u = dx (2a+ 6)°

A: I have use the substitution

Q: +00 dx Evaluate the improper integral x(In x)²

A:

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

A:

Q: dx Using the substitution x =2 sin 0 , evaluate the integral x²V4-x 2

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: We need to evaluate the following integral  I = ∫cos6xdx…

Q: Evaluate the integral. S(e* +8e -*) dx | (e 4x +8 e -x) dx =[(Use C as the arbitrary constant.)

A: Consider the given integral.

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1)

A: The given integral is:∫-2x+4x2+1x-1dxWe need to evaluate the above integral.

Q: (a) Evaluate the integral [x (x* -1) ´dx by using substitution.

A: To evaluate the given integral ∫x3x4-12 dx by using substitution.

Q: Evaluate the iterated integral. (x2 - 8y2) dx dy

A:

Q: In(x) -dx Evaluate the integral m(2)

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Q: Find the integral +C 1 dx x² – 16

A:

Q: Evaluate the integral. B 4х- 3 dx J2

A: To evaluate:

Q: Evaluate the integrals: (d) ∫(lnx)2dx. (e) ∫tan−1(3x)dx. (f)∫cos4(3x)dx.

A: We can evaluate the first two integrals by using  the integration by parts method. To evaluate…

Q: (b) Evaluate the integral | xe * dx. (1- x)?

A: Given : The integral is ∫ xe-x (1-x)2 dx .

Q: Evaluate the integral. (Use C for the constant of integration.) R - 9x In(x) dx x² – 25

A:

Q: [2'e'dx X

A: Given

Q: Evaluate this integral I = ∫ a 0 x^2 √(a^2 - x^2)   dx. Then determine whether the statement is true…

A: Given integral is,

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A: See attached file for a step by step explanation to find the required Integral.

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.