What is the value of the definite integral (2a + 5a? - 2x – 9) dx? Enter your answer as an exact fraction if necessary. Provide your answer below:

Q: S 16x (8x? – 1)³ dx 6x2 dx x3+8

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Q: What is the value of the definite integral | (42 – 4a? - 7x + 9) dx? Enter your answer as an exact…

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Q: (27 dy 7. ソー

A: Definite integration

Q: 1 dx 8 + 8x2

A: Explanation of the answer is as follows

Q: .3 What is the value of the definite integral | (3t? – t – 6) dt? Enter your answer as an exact…

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Q: Solve the following integral using the power rule and then solve for the value of C given F(3) = 5.…

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Q: What is the value of 'h’ in evaluating [ (3x² + 3x – 5)dx, using Simpson's rule, taking 10…

A: The interval is given from 2 to 3 Hence length  of interval is 1

Q: Given ∫(4x5−3x4−x2−2)dx, evaluate the indefinite integral. Do not include +C in your answer.

A: Given ∫4x5-3x4-x2-2dx

Q: In the following equation/s, find the indefinite integral :- see the equation attached here

A: To Find: ∫19z-5-19z+5dz

Q: dy 6. So 1+y+1 6.56

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Q: You are told that S, f(x ) dx= 9 and g(x dx = -2. What is the value of the definite integral ',…

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Q: evaluate the definite integral using the values below. 23 dx = 320, a de = 16, dx = 4 2 34. z da

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Q: Given ∫(−6x5 +5x3 +1)dx, evaluate the indefinite integral. Do not include +C in your answer.

A: To calculate the indefinite integral of the expression -6x5+5x3+1. To integrate the provided…

Q: cln3 S e (In3) 2 -dx 2x +9 e

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Q: бх + 9 dx V6х — х2

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Q: Evaluate the following integral. 2 4 5 dx dy dz -220 245 dx dy dz =| (Simplify your answer.) -22 0

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Q: Choose the most appropriate answer The definite integral: (4x + 14)dx 14)de = %3D O48 O32 60 O 51

A: Now we will find the solution  we know  ,    Integration of Xn dx = Xn+1 / (X+1)  + C   Where C is…

Q: Solve the following integrals with detailed steps: dx a. x²V4+x2 dx (4-x²)7 b.

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Q: Provide an appropriate response. Given fx) dx = 4 and g(x) dx = 2. use properties of definite…

A: We have to solve the integration

Q: Find the value of following the integral: ☎ COS²T -π1+a* S². dx,a>0

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Q: x² 2 :(a² + x²)ž + C 3 15 1 |x*(a² + x?)¿ dx = -

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Q: Evaluate the following integral. 45e dz dx dy -341 4 5e xy² dz dx dy = (Simplify your answer.) -34 1

A: See the details solution in below

Q: Explain why the following integral is improper and then evaluate the integral. x2 2 dx Хе 8.

A: Here we use Fundamental theorem of calculus to solve the given integral.

Q: What is the value of the definite integral | (-4x° – 3x + 3x – 1) dx? Enter your answer as an exact…

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Q: Evaluate the following definite integral: / -3x(-2x² – 1)° dx Enter your answer as an exact fraction…

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Q: Recall that the constant term, C, cancels out when evaluating a definite integral and therefore, the…

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Q: (x S+ 3x? - 4 ) dx 12

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Q: Given that x dx = b² – a² , use this result and the fact that cos(x) dx = 1, together with the…

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Q: S6x-7)(x-3)dx - 3)d 1.

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Q: St 15x(x + 1)(х- 1) dx s(x* +) dx .4 8.

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Q: 2 dx 2 4 + x?

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Q: state what method applies and how one applies it, but do not evaluate the integral:

A: Degree of the numerator =2 Degree of the denominator = 1 Since the degree of the numerator is more…

Q: 3x – 4 What is the value of the definite integral dx? Enter your answer as an exact fraction if…

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Q: Give the appropriate trig sub that would be used to evaluate dx. Do NOT Vx² – 16 solve the integral.

A: Given:     ∫x3x2-16dx

Q: The indefinite integral is given below. ∫(3x3+5x2−23x−45)/(x2−9) dx The expression can be parsed…

A: given,       and this expression can be parsed as,       we have to find value of a, b, c and d.…

Q: Evaluate the following integrals: Show CLEAN AND CLEAR solutions also indicate what rules/formulas…

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Q: Evaluate the following integral. -0.8x dx 3 e S. -0.8x dx = 3 e (Use C as the arbitrary constant.)

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Q: What is the value of the definite integral | (3t2 – t- 6) dt? Enter your answer as an exact fraction…

A: Given,           ∫-133t2-t-6dt

Q: Find the following. Use C for any constant of integration. 5æ4 5 In(|æ|) 8 „2 + C 6 5x³ dx x6 4 5x5…

A: To evaluate the integration.

Q: Evaluate the given definite integral. 4x3 dx 5 2 .3 dx = | (Simplify your answer.) 2

A: (4x3-x35)=5(4x3)-x35(4x3-x35)=20x3-x35(4x3-x35)=19x35

Q: Find the Indefinite Integrals below (Show all work, and DO NOT simplify your answer). (x + 4)² csc?…

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Q: Evaluate the following integrals. When using substitutions, be show to show them explicitly. a) + 5…

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Q: What is the value of the definite integral ∫ 2 0 (2x3+5x2−2x−9) dx

A: The question has not been provided in proper mathematical format. The limits of integration are…

Q: 10. What is the value of the definite integral ∫91−3t−7/√t dt? Enter your answer as an exact…

A: Obtain the value of the definite integral as follows.

Q: x² dx V(a? – 8)5

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Q: Use the indicated substitution to evaluate the integral. • 7/2 dx, x = 7 sin(0) V49 x2 (Give an…

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Q: 863 e- dx r=0

A: Note:

Q: raluate the following integrals. 3x dx dx Hint: Multiply both denominator and numerator of the…

A: Topic:- integration

Q: Evaluate the definite integral.

A: Given:∫-12 10e2x25 + e4x dxFormula:∫dxx2+a2 =1a tan-1xa +C

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.