(D) What is the value of the original integral in terms of x? -30V z2 + 25 X + C 25z

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

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

A:

Q: Express the integral in terms of the variable u, but do not evaluate it. re21 In x - dx; = In x e5…

A:

Q: he resulting integral of dx is ax + b ln x -Arctan +C, where a, b, d, e, and x3-2x2+5x are integers.…

A: b=2

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral 8 x-6 So ²x+8 dx

A: Use fundamental theorem of calculus to evaluate the integral.

Q: Find the complete integral of the equation (p² +g°)x= pz dz dz where p=- q == ду dx

A: Consider the given partial differential equation as p2+q2x=pz, where p=∂zdx,q=∂zdy Rewrite the…

Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: What is the indefinite integral of / 12x + 18 - ) dx ? x3 + 5х2 + 2х —8

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 49 dx .3

A:

Q: (a) Define a substitution variable u and write / x(x +1)*dx in terms of u. Do not solve the…

A: detailed solution is given below

Q: evaluate the integral. a-) x2 2x dx c.) b.) 3 )عو ه dx 5/3

A: use substitution method  for evaluating the integral.

Q: .2 Integrals of the form V1+4x? dx

A:

Q: 20. J 1 (x+25)√√x dx

A:

Q: [(b) find the integral in the interval [1,4] S(3/2 sqrt(x)-4/x^2) dx ].

A: To evaluate the given integral on [1,4]

Q: Evaluate the integral. 4x° V1 – x² dx = 0, NOTE: Enter the exact answer.

A: Given: Let I=∫01 4x31-x2 dx To Find: To evaluate the given integral.

Q: Evaluate the indefinite integral. 1x - 3 dx J (læ2 – 6x + 4)3 Answer = +C

A:

Q: valuate the integral of x(x – 5)^12 dx from 5 to 6.

A: We have to find out

Q: sin y – ex y' cosy

A:

Q: f' (x) dx 2 104. f(x)²

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

Q: (b) Evaluate 1 (x-2)¹/3 dx by using properties of improper integrals.

A: b Given integral is ∫131x−213dx. We have to evaluate the given integral by using properties of…

Q: can i get step by step help please

A: Option (A) is correct. Explanation:

Q: 11 dx x2 +4 Evaluate the improper integral:

A:

Q: dx a proper or improper integral? Why? (x-3)? .3 Is So 1

A:

Q: 1 -dt , find g'(2). V4 +t5 If g(x) =

A: Let's find.

Q: What is the particular integral of the equation (D 2+9) y= x Cosx?

A: Use basic properties and formula, get PI of given equation.

Q: x²+2x+1 dx (x+2)(x−1)²

A:

Q: The sum 5 x) dx + -1, fx) dx can be written as a single integral in the form f(x) dx Determine a and…

A: Given query is to find the single integral fir the expression.

Q: -2 2x Jo x2-4 Só dx (Improper Integral)

A: Let I is the value of given Integral.

Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

A:

Q: Evaluate the integral: a. ∫ex √(1+ex) dx  b. ∫ ((1+ex)2)/(ex) dx  c. ∫ esin2θcos2θ dθ

A:

Q: Evaluate the indefinite integral: dx + C. %3D 6x4

A:

Q: e2z Q5- The value of the integral . Where C is Z = |3 (Z+1)*

A:

Q: In(sin x) d.x 2

A: We need to find whether given integral is proper of improper.

Q: 3x2 dr In evaluating by substitution, if u =x+1 then what will be the resulting indefinite integral…

A:

Q: 5-e xp 2x 2x e du= 2e2x

A:

Q: G(x) = ∫^1vx xt2 dt (1 is the number on top of the integral sign, x on the bottom)

A: Given integral is:Solving the indefinite integral: The antiderivative of a function of the form xn…

Q: Suppose we perform the substitution u=1+Vx in the integral dx . (1+Vx)5 What is the resulting…

A:

Q: In evaluating /x V4- x dx by substitution, if 4 = 4 – x then what will be the resulting indefinite…

A: ∫x4-x3dxu=4-x→dudx=-1→du=-dx

Q: If - 2 f(x)dæ f(x)dx + f(2)dæ – / f(x)dx, what are the bounds of integration for the first integral?…

A: We have to solve the integration

Q: Evaluate the integral of (x^2)/(x^2 + a^2)^3/2 dx

A:

Q: Evaluate the indefinite integral. x2 dx V0.2x3 + 2.7 + C

A: The query is to find the value of the given indefinite integral: ∫x20.2x3+2.7dx

Q: dx -> X-VX dx 12 X-(X) b.) =In (x-1x)?

A: Solve the given integral

Q: calculate the integral in terms of the inverse hyperbolic functions.

A:

Q: 2x2 dx /3 + x² Calculate the integral:

A: Given,          ∫2x23+x2dx

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

A:

Q: çin fxa-lex®dx dx 3?

A:

Q: x4 – x³ – x – 1 dæ - x3 – x² -

A:

Q: 2t + 1 What is the indefinite integral of dt ? t3 -8t + 21t – 18

A:

Q: If the integral of /x + 1 dx from x = 0 to x = y is equal to 14/3 , what is y?

A: Substitution Method is used

Q: Express the integral in terms of the variable u, but do not evaluate it. 14.x-13 dx; u = 14x 13 -…

A: