Evaluating Integrals Evaluate the integrals in 42. sinh ž de | sinh 2x dx 41. 43. | 6cosh 44. | 4 сosh (3х — In 2) da dx tanh dx 45. 46. coth do V3 (--})- sech? ( x csch? (5 – x) dx 47. dx 48.

Q: Use a symbolic integration utility to find the indefinite integral. (Use C for the constant of…

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Q: Find the indefinite integral and check your result by differentiation. (Use C for the constant of…

A: Here is the solution:

Q: (x2 – 1)*(2x) dx

A: Integration by substitutions

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A: Consider the given result as 2≤∫-111+x2dx≤22. Here,  the integrand is integrate over the interval…

Q: Rewrite integral -infinity to 4   x/x-4 dx using limits (a sum of integrals may be required). Do not…

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Q: Evaluating an Improper Integral :- , Determine whether the improper integral diverges or converges.…

A: Given : The improper integral is ∫4∞ 1x ln x 3 dx .

Q: Using Simpson's rule Evaluate the 1 integral of x² - 4 if the lower limit is O and upper limit is 5.…

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Q: 118–121. Verifying indefinite integrals Verify the following indefi- nite integrals by…

A: We have to solve the indefinite integrals

Q: Use a symbolic integration utility to find the indefinite integral. Verify your results…

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Q: 2. Suppose we want to compute the arclength of y = ln x from x = 1 to x = 3. (a) Write out the…

A: The given curve is y=lnx. Let fx=lnx. The derivative of the function is f'x=1x. We have to write the…

Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: Evauate the definite integral. Use an appropriate substitution. Give the exal value as a fraction.…

A: To find : ∫12xx2+13dx Let u=x2+1. Then       dudx=2xdx=du2x ∫x(x2+1)3dx=∫xu32xdu…

Q: Find the indefinite integral by the method shown in Example 4. (х + 7) у3 — x dx Step 1 The given…

A: We will find x in terms of u. u=3-x So, x+u=3 Or, x=3-u

Q: 2. Find the indefinite integral: S 5x²e2x*+3 dx

A: We have , ∫5x2e2x3+3dx we take constant term outside   5∫x2e2x3+3dx Let u=2x3+3 Differentiate  both…

Q: ue of the integral. Explain why the inequality below is true for x > 0. ex e* (sin²x) e2x +3+x² ≤…

A: Given

Q: 2. Suppose we want to compute the arclength of y = ln x from x = 1 to x = 3. (a) Write out the…

A: Solution 1: Given function is y=ln x  from x=1to x=3 So arclength is…

Q: Prove that X+1 Cothx=-In

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Q: x cot x²dx b. J 1+3sin x?

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Q: e cosx sin x dx 1-e2 cosx

A: Given problem:-

Q: Evaluate the integrals . Some integrals do notrequire integration by parts. ∫x3 cos 2x dx

A: Let fx=x3 and gx=cos2x. Tabulate f(x), derivatives of f(x), g(x) and antiderivatives of g(x).…

Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

A: Indefinite Integration

Q: *definite integral from bounds 0 (lower) to pi/2 (upper)* 30cos5(x)dx

A: I solve the above integral using substitution and trigonometric identities.

Q: Evaluate the integrals . Some integrals do notrequire integration by parts. ∫cos √x/√x dx

A: To evaluate: ∫cosxx dx

Q: definite integral from bounds 3(sqrt2) (lower) to 6 (upper)* 1/t3((t2-9)1/2)dt

A: Given integral, ∫326  1t3 t2-9 dt

Q: Area between two curves using definite integrals; 1.y= x2   , y=2x+3

A: solution is given as below:

Q: integral of xcos5x

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Q: 1. /1+ dz

A: The objective is to evaluate the indefinite integral.

Q: Below, we see a region bounded by two curves and the a-axis. The region shaded in light blue is…

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Q: d the indefinite integral. Check your result by differentiating. (Use C for the constant of…

A: Given query is to find the value of integral.

Q: a) The first step is to apply integration by parts, splitting the integral into two appropriate…

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Q: Evaluate the integral. The integral from 0 to t of 9sin^2(x) dx  Then determine whether the…

A: A detailed solution is given below.

Q: Set up the integral that gives the length of the curve y = on the interval (0,8). Use increasing…

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Q: Evaluate the integrals 1)integral of (2sin x + 3cos x)dx

A: Due to our guidelines we can only solve one question at a time . So if you want other question's…

Q: Evaluate the integral.   The integral from 0 to t of 9/(sqrt of 1-x^2) dx   Then determine whether…

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Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of…

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Q: indefinite integral* (26/(x-1)(x2+25)) dx

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Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. 6² × Step 1 x sin 2x…

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Q: 4 dx

A: ∫04dxxFunction f(x)=1xThe definite integral ∫abf(x) dx is called an improper integral if(a) At least…

Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.) x…

A: We have to find

Q: Using Integration by trigonometric substitutions evaluate the given indefinite integral: dy

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Q: Evaluate the integrals . Some integrals do notrequire integration by parts. ∫x3√(x2 + 1) dx

A: Given:  ∫ x3 x2+1 dxUsing the method of substitution:…

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Q: Solve for the indefinite integral of the given. Upload your solution before moving on to the next…

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Q: Concider the area shown, bounded by f(x)=x4 and g(x)= 16x-4x2. Set up the intergral to find the…

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Q: 7. Calculate the integrals. SHOW ALL STEPS required to calculate the integral. Give EXACT VALUES,…

A: Given: I=∫1esec2lnxxdx                                                   ..1 for evaluating given…

Q: Use a symbolic integration utility to find the indefinite integral. Verify your results…

A: The given integral is

Q: he general antiderivative of a function is also called the. A integrand B arbitrary constant…

A: The general antiderivative of the function