Use substitution to evaluate the integral in terms of f (x), assuming f (x) is never zero and f' (x) is continuous. Choose the correct answer. f' (x) dx = f(x) In (|f(x)|) + C - In (|f(x)|) + C - In (f(x)) + C O In (f(x)) + C

Q: Evaluate the integral.

A: Given integral is We will use the following substitution to evaluate the integral.

Q: determine whether the improper integral converges and, if so, evaluate it.

A:

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: Given function ,     f(x)= sin x

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

A: To make the answer in inverse hyperbolic form, do the following substitutions. Substitute x=sint in…

Q: Evaluate the integral or show that it is divergent.

A:

Q: compute the definite integral.

A: ∫1elnx dxx2

Q: Evaluate the integral. inegral  0 to 1    [ (x-4) / ( x2  - 5 x +6 )] dx

A:

Q: Find out if the improper integral converges or diverges. If the given converges, find its value.…

A: Solution

Q: Determine whether the improper integral converges. If so, evaluate it. 6 dx (x-5)3/2 5

A: Here we have,

Q: Use the limit definition of the integral to evaluate the integral 4 3 (4.2 - x²) dx =

A:

Q: Determine whether the improper integral diverges or converges. dx 1.So (2x-1) 7 dx 2. x +1

A: We have to determine whether the improper integral ∫-17 dxx+1 diverges or converges.

Q: Determine whether the integral is convergent or divergent. x arctan(x) 63 dx (1 + x2)2

A:

Q: evaluate the integral (In (X )Ć dx X3

A:

Q: Use Simpson rule’ 1/3 Method with (n = 6) to estimate the integral f(x) = x / ((9*x^3)-3), where a=…

A: Fghhhj

Q: Evaluate the integral of x sin x² dx from x = 0 to x = VT.

A: Given,         The integral of xsinx2dx from x=0 to x=π .

Q: Evaluate the integral. inegral  0 to 1 [(x 3 -4x -10 )/(x 2 -x-6 ) ]dx

A: Consider the following definite integral:…

Q: Determine whether the improper integral converges and, if so, evaluate it.

A: We can write it as: ∫05x-2019dx The given integral is improper because the integrand is undefined at…

Q: Use the comparison theorem to determine whether the integral is convergent or divergent. ∫ ∞ 1…

A:

Q: dx Evaluate the improper integral if it exists

A: The solution is given as follows

Q: 1 Jo 4/7x* +9x³ 1 dx x² +7 x +7 dx 3x° + x³ Jo T3x +x

A:

Q: Evaluate the integral / f(x) dx, where -1 -{ if – 1 < x < 0 if 0 < x < 1 -X - f(x) = 1-VT - x²

A:

Q: 1 Evaluate the improper integral or show that it is divergent. x In x

A:

Q: b. It is known that on the integration interval -1 <x< 3, for the integrand function f (x): 2.2 <…

A:

Q: Evaluate the integral or show that it is divergent.

A: Given: I=∫2∞dxxlnx                           ..1 for evaluating given integral, we substitute lnx=t…

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it converges

A: The given integral is ∫4∞1xlnx3dx.

Q: Evaluate the indefinite integral: 3 dx J x In(5x)

A:

Q: Evaluate the integral. inegral x4 /(x-1) dx

A: Given: ∫x4x-1dx

Q: Determine whether the integral is convergent or divergent. 1 dx x² + x

A: a) limt→∞∫6t1x2+xdx=limt→∞∫6t1xx+1dx Use partial fraction 1xx+1=1x-1x+1

Q: Evaluate the integral, if it exists: +z sinx dx z-

A: We will evaluate the integral if it exists in the following step.

Q: The integral of ƒ In(ln(x))dx can not be expressed as a finite sum of functions. What do we call…

A: It is called as non elementary integral

Q: Determine whether the improper integral converges and, if so, evaluate it.

A: ∫56dxx-532 On integrating, we get ∫56dxx-532=∫56x-5-32…

Q: 1 dx 7x° +9x x² +3 dx 2 2x* +x

A: Explanation of the answer is as follows

Q: Evaluate the definite integral of f(x)=3x^2+2x+ x^(1/2) over the interval [0,1]

A:

Q: determine whether the improper integral converges and, if so, evaluate it.

A:

Q: Show that the integral is either Convergent or Divergent. If it is convergent evaluate the integral.…

A: Given Data The integral is      Using the limit to show the integral is convergent or divergent,…

Q: Use the Fundamental Theorem to calculate the definite integrals. 2 1 dx x+2 -1

A:

Q: Use a summation to find the integral from 0 to 4 of f(x) 2x + 1.  Then check it using the power rule…

A: Integration and derivative

Q: Determine whether the integral is convergent or divergent. *e-1/x dx x2

A:

Q: determine whether the improper integral converges and, if so, evaluate it.

A: Given integral:

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Definition used-        Integral is convergent if the limit exists and a finite number,…

Q: 20. Verify by differentiation that finx dx = x(In x-1) + C, then use appropriate changes of…

A:

Q: An even piecewise continuous function f(x) on every finite interval of (-oo, 0) such that :/ (x)|…

A: The given statement is : An even piecewise continuous function f(x) on every finite interval of -∞,∞…

Q: Evaluate the integral.

A: Given: The integral, ∫12x5lnx dx.

Q: or show that it is divergent Evaluate the integral dx 10

A:

Q: determine whether the improper integral converges and, if so, evaluate it.

A:

Q: Let a and b be non-negative real numbers. Provide an example of an improper integral of the form…

A: Given problem :-

Q: determine whether the improper integral converges and, if so, evaluate it.

A: Write the integrand as exponent of x

Q: dx x (In x)5

A:

Q: use the Comparison Theorem to determine whether the integral is convergent or divergent. ∫∞0…

A:

Q: Evaluate the improper integral if it is convergent. (If it is divergent, type DIVERGENT 7e e-x/2 dx…

A: