Use geometry (i.e., areas of triangles, rectangles, and circles) to find the exact values of each of the definite integrals in Exercises 21-28. (2 – x) dx | 0(4x – 3) dx 21. 22. 23. 24 dx 24. |3х + 1| dx | V1-x² dx Vr2 – x² dx 25. 26. -1

Q: Evaluate the indefinite integral S- dx 3x² x³√x6-1 O 3+C sec-1 +6 O sec-1x3 3 + C ec²¹x² + C sec 3…

A: SOLUTION-

Q: 3. Use a substitution to evaluate the following indefinite integrals, clearly stating the…

A: We will solve the problem

Q: Use properties of the integral and the formulas in the summary to calculate the integrals.

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Q: (8 - 3x2) dx. Given that dx = use this fact and the properties of integrals to evaluate

A: Given: ∫01x2dx=13 The objective is to evaluate the integral of ∫018-3x2dx

Q: -0.5 3. f5 x(1-x)³ dx 0

A: To evaluate the given definite integral by using substitution rule.∫00.5x1-x3 dx

Q: Question Using integration by parts, the integral f In(8x²) dx is equal to:

A: Please see the answer in Step 2

Q: x+4 dx Vx

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Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral x³Inx A x² dx 3 O ---fa…

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Q: Calculate the indefinite integral x²sin(x)dx Show your calculations.

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Q: -1 dx -2 x²+1

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Q: Using reciprocal substitution x=-, the integral -dx reduces to (z- 1) 1/3 © -/t- dz 1/3 © - /(?-1)…

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Q: 4. Evaluate the integral sin x cos x dx by two methods: first by letting u = sinx, and then by…

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Q: Evaluate the integral 6. dx x2 V16x2 – 9 | Note: Use an upper-case "C" for the constant of…

A: Solve the given integral

Q: 2х2 -бх+4 dx X-3

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Q: / (22* + 3,/5 +) Calculate the indefinite integral: dz

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Q: Evaluate the definite integrals using properties of the definite integral and the fact that 5 5 S √³…

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Q: e2X dx V1+e2x

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Q: Use geometry to evaluate the definite integral. 22 x dx 22 -x dx = | (Type an integer or a…

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Q: 9. f(x³ - 4x)dx -3 (x²-1) dx 10. ₂

A: We have to find the integral

Q: 62-a2 x dx = cos(x) dx = 1, together with the properties of definite integrals, to evaluate (2…

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Q: 53

A: Given

Q: Use properties of the integral and the formulas in the summary to calculate the integrals.

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Q: How does the method of substitution work for definite integrals? Give examples.

A: To elaborate the use of substitution for computing the integrals with example.

Q: 02:- By using integration by part, find :- (Choose two only) 2-f Inx (x') dx

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Q: (x² – 1)*dx

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Q: Evaluate the integral 8 dx x² V25 – x2 Note: Use an upper-case "C" for the constant of integration.

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Q: Evaluate the definite integrals using properties of the definite integral and the fact that dx = -5.…

A: Since, we only answer up to 3 sub parts, we will answer the first 3. Please resubmit the question…

Q: Use the Change of Variables Formula to evaluate the definite integral. 1 dx V3x + 5 (Use symbolic…

A: Given:       ∫0413x+5dx      substitute u=3x+5→dudx=3→dx=13du            =∫0413udu taking constant…

Q: dx x²-x-2 ーズ

A: Given integral, ∫2x2-x-2dx

Q: (8 - 3x*) dx. x² dx use this fact and the properties of integrals to evaluate Given that

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Q: Use integration by parts to evaluate the integral. (Use C for the constant of integration.) In(5x)…

A: Given , the integral We have to evaluate the integral by using by parts formula.

Q: 20/x² – 49 -dx - Evaluate the integral: (A) Which trig substitution is correct for this integral?

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

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Q: Use substitution to find the indefinite integral. 5х +6 -dp- (5x2 + 12x) 3 S- 5x + 6 dx = 3 (5x2 +…

A: Given:Here f(x)=5x+65x2+12x3 To find:we have to find the integral by using substitution

Q: Evaluate the integral. (Use C for the constant of integration.) 7-6x - x² dx

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Q: x²-x-8 /hat is the indefinite integral of (2x – 3 )(x² + 2x + 2) dx

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Q: FInd the Indefinite Integral and check the result by differentlation. 6x dx 8 - X Step 1 is the…

A: We have to find solutions

Q: За? +8х —12 dx x3+7x²+12x 3x +8x- -12х

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Q: In Exercises 35–38, guess an antiderivative for the integrand function. Validate your guess by…

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

Q: Q3: Use integration by parts (Tabular method) to find the integral (r³_2 x² +3x +1) sin(2x) dr

A: The given integral is ∫x3-2x2+3x+1sin2xdx To solve the integral using by parts .

Q: Use integration by parts to evaluate the integral. (Use C for the constant of integration.) In(4x)…

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Q: Em hake 3 an

A: We can find the integral as below

Q: Use the Change of Variables Formula to evaluate the definite integral. 4 dx V5x +3 (Use symbolic…

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Q: Evaluate the integral -3 dæ x² + 16 Note: Use an upper-case "C" for the constant of integration.

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Q: Use one of the formulas in the table above to integrate dx x8 + 16 (By the way, you're going to need…

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Q: Find the indefinite integral.

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Q: Use residues to find the indefinite integral f* dx- (16+x)2 2x2

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