5. S,(x-4)(x2-8x – 1)3

Q: A. Evaluate each of the following indefinite integrals: S*(1+v*) -ldv (cor-ly2) 2.

A: Solution is given below:

Q: Evaluate the following definite integrals.  1. ∫04 (3x - (x2 / 4)) dx 2. ∫-11 ((√3x)-2) dx 3.…

A: Q 1. Consider the definite integrals: ∫043x-x24dx To solve the given integrals: ∫043x-x24dx=∫043x…

Q: 5. Evaluate the definite integral (1+Inx) а. b. S dx. 2x+3

A: a) ∫1e1+ln x2xdxb) ∫-1112x+3dx

Q: 2. Evaluate the following definite integrals: S dx -22-x b. S32 sinx dx а. С.

A:

Q: 4 Suppose | f(x)dx = 6, f(x)dx= 5, and g(x)dx = 8. Evaluate the following integrals. g(x)dx = 7…

A:

Q: 3. Find each of the following integrals using any suitable techniques : sin 2x dx cos4 2.x (c)

A:

Q: 9. √x SOL -√√x dx

A: We will solve the given integral using simple Integration rules.q

Q: 7.1: Evaluate the following integral and show your work: S (2? + 1) e-" dæ, 0 < x < 1 е

A:

Q: 4. 13x²-1 3 X-X -dx

A:

Q: X 17. 7. So (x²+ + 2)² dx

A: Topic = Integration

Q: [sin(In x)+cos(In x)]¯ dx

A:

Q: 1. Which of the following integrals is a candidate for the Substitution Method? | 5x* sin(x*)dx sin'…

A:

Q: By-1 dy 2y+1

A: We have to solve given indefinite integral.

Q: 25. Evaluate the following definite integrals. c) Li VIXI – x dx dy d) L (y+2)3 e) L, 3wv4 – w? dw

A: there are 3 separate question but according to bartleby guidelines i am supposed to solve only 1

Q: Evaluate the definite integral. 3 3 dy y /1

A: As per bartleby answering guidelines we are allowed to answer only one question per post. Hence…

Q: Q1 - Find the reduction formula for each of the following integrals iv. In = S sinh"x dx

A:

Q: dx (16+x)³3/²

A:

Q: How do I find K of the integral e^(x^2/2)dx on the bounds from 0-2 what is E_T? and what must n…

A: Given: The error in trapezoidal rule is given as:

Q: Write down an explicit solution (involving a definite integral) to the following IVP.  a. y'=…

A: See the solution in the given fig. 1 and fig.2

Q: 6. Evaluate following definite integrals: S(3x2 +2x – 2) a. b. (3x + 2VA)

A: Given  a)∫15(3x2+2x-2)b)∫49(3x+2x)  Let us evaluate the first integral (a)let…

Q: 18. ydy 5-y

A:

Q: [2 + s= 1 Lx-a (x-a)k] dx

A: Explanation of the answer is as follows

Q: 7.) Evaluate the following definite and indefinite integrals a.) ò (5-2x* -2x*-cos.x)dx +6x)dx b.)

A: Follow step 2

Q: y3 dy |(1– 2y*)$

A:

Q: 7 For the integral 3xVx + 6dx, if we use the substitution u = x + 6, we can rewrite the integral in…

A:

Q: 3. Solve the following integrals: a) f(5x+2)³¹dx

A:

Q: 1. Use properties of the definite integral to solve the following problem. f (x)dx = -3 and f(x)dx =…

A:

Q: 12. Evaluate the integral. x² – 4 – dx

A:

Q: ܐܐ 19. dz 'z(nz5

A: The given definite integral is ∫122 dzzlnz1/5. Solve the definite integral by the substitution…

Q: 3. fx² √9-x² dx

A:

Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

A:

Q: -2 Evaluate the definite integral S: 1 dx. 1 x+a²

A: general answer is Ln|(2+a^2)÷(1+a^2)| Where a = -3/5 Final answer is Ln|59/34|

Q: 6 Use the properties of definite integrals to find f(x) dx for the following function. 1 2x + 1 if…

A: Given that, f(x)=2x+1          if x≤5-0.3x+7    if x&gt;5 We have to calculate the value of…

Q: Q4. Find the integral of the following functions x dx (x-1)(x2+2x+1)

A:

Q: 25. Evaluate the following definite integrals. e) L, 3wv4 – w2 dw

A:

Q: 3. Evaluate the definite integral below: S¯¼ √x² + 2x − 5dx + Sq − √x² + 2x − 5dx

A: To solve the following integral problem

Q: 13. Evaluate the definite integral. 1 а. x6 b. (4x – 1)²dx = С. 7 du = Vu n. d. 2 e. (13 – t3). dt…

A: Here we have to evaluate the given definite integral.

Q: 1. Find the following indefinite integrals. 1 (а) xp /3 – x²

A: We can find the integrations as below

Q: 1) Find the indefinite integral of the following functions: 3 2x+ 3x4 a) y = Axt B 3 b) y =x-1 +…

A: Indefinite Integration

Q: 6. dx 13+4x- ?ܢ

A: A detailed solution is given below.

Q: 1. Evaluate the following integrals. Do not simplify! (a) S 7x(3x² + 5)'14dx

A: Given that a)∫7x(3x2+5)14dx b)∫x-3x+8dxc)∫x(4x-1)6dxWe need to evaluate the integral

Q: 25. Evaluate the following definite integrals. dy d) (y+2)

A:

Q: 3: Evaluate the following definite integrals. / (2x – 62² + x°) dx

A: NOTE: You have posted multiple questions at a time, we have given the answer to the first…

Q: 16 Suppose we know that " (35(x) – 2) dr = 6 and that :[ #f(x²) dx = 8. Use this information and…

A: We have, ∫4163fx-2dx = 6 ∫04xfx2dx = 8 To evaluate: The value of ∫04fxdx

Q: 9. Evaluate the following definite integrals. S" V5x – 1 dx 10 а. b. J sin 2x dx

A:

Q: (8) 18. Evaluate the following indefinite integrals: (a) / (5e* +7z + 1le") dr dr

A:

Q: /4 1.* Use the following property of the definite integral to estimate the definite integral:JCcos x…

A:

Q: 2. fx²5-x' dx

A: ∫01x25-x3dxapply u substitution;take, u = -x3;du = -3x2-du3=x2then our equation can be written as…

Q: —3г — 7 What is the value of the definite integral dt? Enter your answer as an exact fraction if…

A:

Q: 9. Which of the following integrals can NOT be computed using the methods we have covered so far? a)…

A: We have to choose the integral which is not compute by simple integration method

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.