(x + 2) dx (x² + 4)(x – 2) B) Use the techniques of integration to evaluate

Q: Evaluate the integral. (Use C for the constant of integration. x² 3/2 dx - 4x²)2 3 + 4x

A: We have∫x23+4x−4x232dx

Q: Q2.Use Triangular method of integration, find the integral f dx. √√x²-9 5x4

A:

Q: cln 2 re dr. Use integration by parts to evaluate

A:

Q: dx (4x²-9)

A:

Q: 16. dx x√√16+x²

A: To find out the integration.

Q: a) Evaluate the indefinite integrals using Repeated Integration by parts i) fx²e-2*dx ii) fx?Sinxdx

A: We have to evaluate the given integration.

Q: Evaluate the integral. (Use C for the constant of integration.) 7x2 + x + 7 dx (x² + 1)2

A: The given integral is: ∫7x2+x+7x2+12dx To evaluate the given integral.

Q: dx √2+√x −1 14. f-

A:

Q: In(2 x) dx =; x³ In( 2 x) - +C x e dx = -2 (2 +x) e +C

A:

Q: Evaluate the integral. (Use C for the constant of integration.) +² | dx 81-x²

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | (4x4 - 3x-2 + 5x-5 + 2) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (x6 − 6x2)4(x5 − 2x) dx

A: From the given problem:   I=∫x6− 6x24x5 − 2x dx...(1)   First simplifying:…

Q: (b) Use Integration by parts to show that ·4 In x ~dx= =-+2ln.x) +C

A:

Q: Using Variations on the substitution method Find the integral

A: To evaluate integral ∫xx+1dx Let x+1=t Differentiating both sides with respect to x,…

Q: dx x+x4/3

A:

Q: Find the indefinite integral using the Chain Rule/U-substitution. 6x dx x2+5 3. 4. S 7xv3x² + 8 dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | (4x* - 2x-2 + 3x-5 + 5) dx

A:

Q: Use integration by parts to find the integral. (7x-3) e-2x dx -2x dx = (7x-3) e

A:

Q: Evaluate the integral –4x3/2 In(x) dx, x >0 Note: Use an upper-case "C" for the constant of…

A: Evaluate the integral

Q: Evaluate the integral. (Use C for the constant of integration.) (4x4 3x-2 + 5x-5 + 2) dx

A: By using integration formula we can easily solve it. See attached file for a step by step…

Q: Evaluate the integral. (Use C for the constant of integration.) 1- 36x2 dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9xV1- x4 dx

A: Formula used: ∫a2-x2dx=xa2-x22+a22sin-1xa+C Calculation: Simplify the integral as follows:…

Q: Evaluate the integral. (Use C for the constant of integration.) 5xV1 - x4 dx

A:

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?

A:

Q: Using integration by parts, | - | x sin(x²) dx x* cos(x²) dx = k – Then k is?

A:

Q: 11.f (4x+5) dx √1-2x

A:

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

A:

Q: (a) Using integration by parts, find fx sin(2x - 1) dx. (b) Use substitution method to find x² 2x-1…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) a + bx5 dx 6ax + bx6

A: Given the following integral:

Q: Evaluate the integral. (Use C for the constant of integration.) x2 + 16x + 1 (x2 + 1)2…

A: We have to find integral.

Q: Evaluate the ∫ from 0 to 1 of xe−2x dx using integration by parts

A: Given, I=∫01xe-2xdx

Q: 6 -dx Jx? - 5x+6 What integration technique would you use on Find the integral. Show every step.

A: To find the below integral. ∫6x2−5x+6dx

Q: Evaluate the integral. (Use C for the constant of integration.) dx 3 - 3x9

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 3 + 2x - x2 dx

A:

Q: By using integration by parts, one can prove the reduction formula. | (In(x))" dx = x(In(x))" – n/…

A:

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

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 11 dx x²V 4x² - 1

A: Given integral ∫11dxx24x2-1=11∫dxx24x2-1 Now consider ∫dxx24x2-1 Use substitution method to solve…

Q: Use integration by substitution and the Fundamental Theorem to evaluate the definite integral. 2 |…

A: Use substitution method

Q: dx 1+x-2

A:

Q: 7. Evaluate the integral. (Use C for the constant of integration.) √x² - 25 x² - dx

A:

Q: Evaluate the integral -1 dx x² + 16 Note: Use an upper-case "C" for the constant of integration.

A: LetI=∫-1x2+16dxTake the constant out:  ∫a·fxdx=a·∫fxdxI=-∫1x2+16dxI=-∫1x2+42dxPur x=4tany…

Q: Integral / 142°. | | 14.x? – x³ – 45x| dx MUST be evaluated by breaking it up into a sum of three…

A: In this question, we evaluate the value of definite integral by finding the critical points of the…

Q: Evaluate the integral. (Use C for the constant of integration.) 9x dx x4 + x2 + 6 + X'

A:

Q: Evaluate the integral. (Use C for the constant of integration.) dx 49 - x2

A: We have to find the integral

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: dx (5-4x-x²) 18. 8. f

A:

Q: Evaluate the integral 1 dx x4 – x2 Note: Use an upper-case "C" for the constant of integration.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx xV 9x2 - 1

A:

Q: (3x-3) dx (x²-2x+1)(x²+2x+8)

A:

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.