|| es / MATHT02-AIl dx x244 ²+3 In 13 2+2 In

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

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Q: (In 10x+4lnx) "dx Identfy the correct u A Inx B In°x+4 In x

A: topic- definite integral

Q: 14. Consider that * Sof (x)dx = 2 and f'(1) = 3. Find Soxf"(x)dx. %3D 3 O 5 O 1 O 4 O 2

A: We have to find

Q: b 1+ e2x Evaluate the integral. ex xp 1 + e2x

A: Given that: ∫01ex1+e2xdx

Q: 35 - A 3x7 matris ve rankA = 3 ise nullity A = ? O A) 4 O B) 3 OC) 1 O D) 0 O E) 2

A: Answer (35) Given ,  A 3×7 matrix where rankA = 3  We have to find nullity A

Q: Evaluate In x dx x3 А. In x x3 1 In x 2x2 1 + C 4x2 В. In x dx 1 1 x3 In x - 2x2 4x2 + C С. In x dx…

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Q: In 8 In y e**y dxdy S S Q2. Evaluate 1 0

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Q: 3. x In x A In С п IInxI + С - + C Inx B D In I In xI + C Inx

A: ∫πx ln xdx

Q: Evaluate / (In(x) -)dx Oc – 5 In(x) Oln(|In(x)|) + c 05 In(x) + c O5 In(|In(x)|) + c

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Q: d Prove that (x") = n x"-1 dx

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Q: 25-x² dx In if we let u = V25 – x , then udu =-xdx.

A:

Q: 7. Show that Sx" Inx dx =Inx-+ c. n+1 %3D + C. n+1 n+1]

A: Using integration by parts we can prove the given integral.

Q: 18. y = (In 0)" > dy de = T(In 0)-1) () T(In 6)(-1) %3D

A:

Q: Solve the integral: A In/1+ B -In|1+ x 5. 1 3X + C + C 5 x X + X x dx

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Q: ()- d - en In x (en In x )(n)| = n(x")(x=l) = nx"-1 87. dx

A: Given information: The function enlnx Chain rule of the derivative, ddxefx=efxddxfx

Q: 19. f' "'In rdr r'In r dr

A:

Q: d) f(2) = In (In z)

A: As requested 4(d) to be solved 4(d) fx=lnlnx

Q: In|In x| + C 2.STinx dx x In x 1 3/x +C 3. S dx

A:

Q: dx = O In|æ| + C O In(x) + C O z° + C O Does not exist.

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: 12. Find the integral of S (x². √(x² + ² =) dx

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Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: Evaluate the integral dx (8x + 3)3 by making the appropriate substitution: u = 8х + 3 dx (8x + 3)3…

A: Recall:    ∫un du=un+1n+1+c ; where c is an integration constant.

Q: Evaluate the integral.

A:

Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

A: I am attaching image so that you understand each and every step.

Q: 15% at Goldstein's. A pric riced at $119 He a

A: Given, Cox's and Goldstein's department stores give discounts to college students, 10% at Cox,s and…

Q: Evaluate the integral: S(6 + 5x) dx dy 22 44 O 4 O 2

A: Double integration

Q: 10. Find the integral of dx x²-4 O In() + C x-2 O In() + C 2x x+2 O fIn( *2) + C X+2 O In() + C x+2…

A: *using concept:- 1. Partial fraction. 2. int(dx/x) = ln(x). 3. ln(m) - ln(n) = ln(m/n).

Q: de xdx 1. (In* 4x-1) 2. V3x +5 sin 4x de de 4. 9+8cos 2x 3. (5x-3)dr 5. 3x-3x+2 (3-4x)dx 6. TAx…

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Q: 1. (a) Prove the following. | (In x)"dx = x(In x)" – n (In x)-' dx

A: To prove that 1.a. ∫lnxndx=xlnxn-n∫lnxn-1dxb. Using 1.a compute the following      ∫lnx3dx

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: 2) Show that L(1-x*)P",)P"mx) dx = 21(1+ 1) Sim 21 +1

A:

Q: 2.Evaluate the following integral: √3x² cosxdx (d) single application of Simpson's 3/8 rule.

A: Here we can take N=6 ,that is number of interval =6. Then we can use Simpson's 3/8 rule to find…

Q: Evaluate (а) S In(2.x + 2)dx -1

A: Given:          (a): ∫−11ln(2x+2)dx

Q: x2 1 dr dy = a° In(1+ x² + y? 3

A:

Q: 3. Obtain the 6.S. sy dx + taydy = 0 xcos

A: We have given equation  xcos2y dx+tany dy=0 xcos2y dx=-tany dy x dx=-tanycos2y dy x dx=-sec2y tany…

Q: 5. Evaluate : p.v en dx -∞ (x²+3)²

A: Using complex contour integration

Q: et + 6e3t + 12e2t +9e dt. (d) Evaluate the integral / (e2t +4et +5)2

A: First, simplify the integral. As the degree of the numerator is greater than the denominator, use…

Q: 3. Prove that So 0 1 x + ex -dx = n=1 (−1)n−1(n − 1)! nn

A:

Q: (b) Evaluate In(x) dx 1

A: The given integral is divergent.

Q: Evaluate the integral. S20 2 cos 4x dx 3 O A. 4** 1 sin 8x + 1 sin 16x + C 16 +X. 3 1 O B. 7x+3 sin…

A:

Q: Evaluate the integral: Sen(+²+2x-7) ox dx A x² + 5x + In|3x-6|+C B +5x+31n|x-2|+C X + +In|3x-6|+C Ⓒ…

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Q: Determine the integral of the ff. fun 1. S- 6 dx 2. S 5 x4 dx 3. S ( 4 x7 + 7 ) dx

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Q: In x + In(x – 1) = 10 In(x + 25) – In(x – 1) = 3 e2x – 2ex = 15 e2x – ex – 12 = Q %3D %3D -

A: i) ln x+ln(x-1)=10ii) ln(x+25)-ln(x-1)=3iii) e2x-2ex=15 Note:      Multiple part question are given,…

Q: Evaluate the double integral: S²² (3x² +9y²) dxdy 0

A:

Q: Evaluate the improper integral s dx -2 (2+1)4/3

A: Given: To evaluate ∫-201(x+1)43dx

Q: 2s+2 ds = In|s| – In\s + 2| + C %3D s3 +3s2+2s

A: Here, we are solving only 1st question and for the remaining question post the question again.…

Q: 23: Evaluate the integral of ſ (5y+7) 5 dy

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Q: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

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Q: Evaluate ſ dz j d ſ e dy. O 8/3 O 8e-8 O 8e/3 O8

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

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.