Evaluate the integrals in Exercises 12s + 5) ds (8s³ 78. 77. 4x + 7) dx

Q: evaluate the integral using the methods covered in the text so far.

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Q: Compute the integral ∫dx / 5sinx+2cosx+2.

A: Apply t substitution

Q: What should be the rewrite of the integrand of (2x + 5)² dx so that the resulting integral is…

A: Topic = Integration

Q: (x²–16)3/2 -dx x3

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Q: Use any method to evaluate the integrals in Exercises 55–66. x³ – 2x² – 3x dx x + 2 x + 2 - dx x³ –…

A: 55 consider the given integral    Then it can be written as

Q: ydy J-7-By-y

A: Given problem:- ∫ ydy/√(-7-8y-y2)

Q: Use integration by parts to evaluate the integral: fam -1 xdx

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Q: Use integration by parts to evaluate the integral: fin(2) - V/="da = ,11

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Q: Evaluate the integrals ∫2tan x sec2 x dx

A: Now put

Q: Evaluate the integrals in Exercises 33–36. x dx 9 – x2 dx 33. 34. x(9 – x²) dx dx 35. 36. 9 – x? V9…

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: In Exercises 45–48, calculate the integral, assuming that •5 .5 f(x) dx = 5, 8(x)dx 12

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Q: sketch the region of integration, reverse the integral and evaluate 4-x 2 23 4-9

A: Consider the provided question,

Q: 2 B. Evaluate | (2- x) dx by interpreting the integral in terms of area. -1

A: Topic = Integration

Q: ( 3.x³ – 2x³ + 5x² – 2 x3 + 1 dx

A: Given integral is improper fraction form so we need to apply long division method to convert it into…

Q: Use integration by parts, together with the techniques of this section, to evaluate the integral.…

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Q: x2 dx 3 (9- х2)2

A: sin(x)=1-cos2(x) tan2(x)=sec2(x)-1 ddxsin(x)=cos(x)

Q: Estimate the error in approximating the integral from 1 to 3 2x^3dx with n=4  by using the…

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Q: Evaluate the integral

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Q: 4 dx x4-1

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Q: Evaluate the integral. HINT: [Use a shortcut.] 52x - 1 dx

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Q: Evaluate the improper integrals in Exercises

A: Solution:Given59.∫0∞ x2 e-x dx60.∫-∞0 x e3x dxFormula:(xn)'=nxn-1eax'=a eax∫eax dx=eaxa+C

Q: integral

A: We have to choose the correct option from the given options according to the given information

Q: Evaluate the integrals in Exercises

A: 47. ∫sech2x-12 dx48. ∫ csch25-x dx

Q: 10 dx 4x3 –4x²+5x

A: We need to find ∫104x3-4x2+5xdx. So,…

Q: can you invent an exercise of double integrals over shaded regions? (show the exercise and solve it…

A: Solution is given as below:

Q: Evaluate the integrals in Exercises using integration by parts.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 7. (x² - 2x + 3)dx 5²

A: SOLUTION-

Q: In Exercises 45–48, calculate the integral, assuming that •5 .5 f(x) dx = 5, 8(x)dx 12

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Q: | (In(5æ)) (In(5x))²dx

A: We use the by parts method ∫(ln(5x))2dx…

Q: Q4 Evaluate the double integrals:

A: We have to evaluate the double integral. ✓✓(x+y+1)dxdy

Q: Find the area of the triangle with its vertices on the points (5, 1), (1, 3) and (-1, -2) by means…

A: On solving this we will get:- Option (D) -12 sq. Units is correct

Q: Evaluate the integral ∫(5x -1)2 dx by two methods: first square and integrate, then let u = 5x - 1.

A: To evaluate the integral ∫5x-12dx

Q: Explain the application of triple integral in detail ?

A: Triple integral is used to find volume. For volume there should be three dimensions that's why by…

Q: What should be the rewrite of the integrand of dx so that the resulting integral is integrable?.…

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Q: fxcsc² x dx

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Q: –6x-'dx

A: Follow the procedure given below.

Q: - 1₁₂ (3+√4-2²³) dx -2

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Q: 3. Approximate the integral -dx using 4 trapezoids.

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Q: V9x² – 5 - dx . .2 fact to determine the integral 9x?

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Q: Use integration by substitution and/or by parts to compute the integral Jx In (5 +x)dx .

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Q: Evaluate the integral. [HINT: Use a shortcut.] 2-x + 1 dx 35 - d

A: Explanation and solutions is given below....

Q: 2-V1-x dx by interpreting the integral in terms of area. -

A: ∫-112-1-x2 dx On simplification, we get ∫-112-1-x2 dx=∫-112 dx-∫-111-x2 dx   →1 Now consider, ∫-112…

Q: Use integration by parts to evaluate the integral: fam tan-xdx

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Q: 10. f3, (x²-1) dx

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Q: integrals

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Q: Use the Table of Integrals to evaluate the integral. 7arcsin (VI) dr

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: In Exercises 33–42, use properties of the integral and the formulas in the summary to calculate the…

A: Compute the value of the given integral as follows.