B) Evaluate the following integrals: 1) S (x-2)3 dx x²-4 dr

Q: ) Evaluate the following integrals. 16x x4+3x2+1 3 + 24x dx (a) 0,

A:

Q: Evaluate the following integrals. Show your complete solution. 1. S(15x* – 6x² + 2)dx 2. S(VE-)dt

A: The given integral,1. ∫(15x4-6x2+2)dx2. ∫t-1tdt

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

A:

Q: Evaluate only four integrals of the following integrals: 1/4 1 dx (i) dx (ii) J √1-9x² sin (3x) 0…

A:

Q: Determine the following integral: 3x + 3 dx x2 + 7x + 12

A:

Q: Vx +1 dx Vx – 1 3 3 X,

A:

Q: 14 Find the integrals using integration by parts. a. fx(x + 4)°dx c. fr'e"dr

A: As per our guidelines I am solving only first three parts of the question please resubmit the other…

Q: Evaluate the following integrals 3x dx (x2 – 4)2 4. dx b) (3x- 2)*

A:

Q: dx 1. 9-x^2

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Use the value of the first integral I to evaluate the two given integrals. 3 9 4 3 (8х-2x3) dx b. J…

A:

Q: Q1. Evaluate the following Integrals 1 dx xVx

A:

Q: Evaluate the following integrals: 2. Inx de sin 3x 3. dx 1-cos 3x 4. S 32* dx 5. S(e* + 1)°e*dx 6.…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Evaluate the following Integrals. dx V1 – 4.x2 4. -

A:

Q: Evaluate the following integrals a) dx J (2x - 1)3 6x dx b) 2.

A:

Q: 3 Calculate the integral: dx x² V25 + x2

A: Here first put x=1/t and then the expression inside the square root as y^2. As showing in solution

Q: Evaluate the following integrals (2х — 5) 4. dx 2 4x - 4x + 26) | TC 2 1 5. do esc°(20) sec²(2 csc…

A: As you have posted multiple questions so I will answer only first question as per guidelines.

Q: 23/ Choose the correct answer to evaluate the following integral dx 1 - Jo (1 – x+)ż

A: By using Bita gama function

Q: 3. Evaluate the following integral 5x+1 -dx (x-4)(x+2)?

A: Use the partial fraction method 5x+1x-4x+22=Ax-4+Bx+2+Cx+225x+1=Ax+22+Bx-4x+2+Cx-4 Put x=4 21=36A…

Q: Q2 – Evaluate the following integrals. iv. S(secx – tanx)²dx

A:

Q: B- Evaluate the following double integrals: .2 .4 1) | (x+ 3y x²)dy dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the substitution technique to determine the following integrals:

A: Important integrals for the question: ∫sec2 x dx = tan x + c ∫un du = un+1/(n+1) + c Other important…

Q: Use the value of the first integral I to evaluate the two given integrals. 3 | - 27 (x3 - 6x) dx =…

A:

Q: Calculate the following integrals. I (b) /2 I sec rdx-

A: The given integration is  I = ∫xsec2xdx

Q: Given the integral J6x2 - 4x dx бх2 - 4х

A: Complete the following question involving basic integration techniques. Given the integral…

Q: Evaluate the following integrals. 1. sec-a dæ cos Va dx Væ csc /æ 2. x2 dx - 3.

A: Integration by parts

Q: Q1 - Evaluate the following integrals ii. S dx Jo ix-1|

A:

Q: Either evaluate the following improper integrals or show that it diverges. +oo 1 (i) - dx +oo (ii) 2…

A: We have to evaluate the given integrals.

Q: evaluate the integral.

A:

Q: Use the substitution technique to determine the following integrals:

A: Let,

Q: 2. 21-/9 – 4ª dx

A: The by parts method is given as ∫uv=u∫v-∫u'(v) where u is the first function and v is the second…

Q: (1 – 3|x|) dx -2

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Evaluate the following integrals. b. "f2 sec² xdx (2x+5)dx

A: Topic:- application of integration

Q: Evaluate the following integrals: x +1 1- dx (x² + 2x + 2)3

A:

Q: Evaluate the following indefinite integral. dx xV 4x2 – 1 ||

A: Given, ∫dxx4x2-1  We have to evaluate the indefinite integral.

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: We have to find

Q: Evaluate the following integrals 1 (2x – 1)ª dx 6x b) dx V – 4

A:

Q: Calculate the following integral: 4 I V16 - x dx .2 0.

A:

Q: 9. dx V1-x2

A: You must have the idea of basic of integral. The explanation part is given below.

Q: Evaluate the integral. /x + c dx

A:

Q: Evaluate the following integral xe -dx J 1+2ex?

A: The given integral is I=∫xex21+2ex2dx Solving the integral using substitution.

Q: Q1 - Evaluate the following integral: J (2x-3x+2) dx (x-1)2 (x-2)

A:

Q: х-1 dx х3—x2—2х

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Evaluate the integrals: (d) ∫(lnx)2dx. (e) ∫tan−1(3x)dx. (f)∫cos4(3x)dx.

A: We can evaluate the first two integrals by using  the integration by parts method. To evaluate…

Q: Evaluate the following integrals 3 dx a) , -1 3x-2

A: ∫−103 dx3x−2Let t=3x−2dtdx=3⇒dt=3dxAs x=−1→t=−5As x=0→t=−2

Q: Evaluate the following integrals: а- T/2 2cosx dx 1+ (sinx)² -T/2

A:

Q: Evaluate the following integral. 16 dx 1- vx 16 dx | (Type an exact answer.) 1-

A:

Q: Evaluate the integral. X √ ² ₁x + (x + 16y) dy

A:

Q: Evaluate the integral. 10 r FIL √16 22 1 (x² + y²) 1/2 dy dx dz =

A: To evaluate the integral ∫04∫-44∫-16-x216-x21(x2+y2)12dydxdz

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.