Evaluate the following integrals using the appropriate technique. dx (a) S (b) Sp5lnp dp 5-3x

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

A:

Q: 4. Sx 2* dx

A:

Q: Evaluate the following integrals.

A: Given integral:

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

A:

Q: Evaluate the following Improper integral: +00 dx x2 + 2x + 4 8.

A: We will evaluate the following improper integral.

Q: dx 8. J3 x-3)3/2

A:

Q: 4. dx (x² +1)*

A:

Q: Find the indefinite integrals, if possible, using the formulas and techniques.

A:

Q: Evaluate the following integrals using dx = -00 (a) 7xe- dx (b) 13 xe-X dx

A:

Q: Evaluate the following integral by appropriate method: L 12x – 1| dx

A: Given integral is

Q: Evaluate the following integrals.

A: Integral is ∫x-2+x-3x-1+16x-3dx

Q: |Q1 - Evaluate the following integrals i. 2x+5 •dx x2+3x-10

A:

Q: 1. x +4 √x -dx

A: We will use substitution method.

Q: V4x2 + 9 dx (a)

A: Given :         ∫4x2+9x4dx

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

A:

Q: EVALUATE THE INTEGRAL: dy x 1+2x3410

A:

Q: For what values of K is the following integral improper? 5x dx x2 - 19x +90

A:

Q: Evaluate the following integrals: (i) S(x² + 1) e-3* dx x5-2x2 (ii) S; Vx6-4x3

A:

Q: 2. dx 1+√√x

A: integration

Q: Evaluate the following integrals using the tabular method. (i) (ii) (3x³ – 2x² + 1) sinh 2x

A: Evaluate the integrals using tabular method.i) ∫e2xsin2x dxii) ∫3x3-2x2+1sinh2x dx

Q: [x² (-2 + x² )* dx

A:

Q: Q2) By using a division method. Evaluate the following integrals: y?tan-'ydy

A: To find the integration

Q: dx (6-x²)3/2 TT

A:

Q: dx Vx²+2x+5

A:

Q: Evaluate the following integrals. 9 – x2 dx - 1.

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Q: Evaluate the following integral by completing the square: dx . x +6x + 13 .2

A:

Q: dx J 2 + Vx

A:

Q: Evaluate the following integrals -3r (r+y²)dydx

A: Given query is to eveluate the integral.

Q: Find the indefinite integrals below. a) S 12x³ Vxdx dx x³-7 b) S c) S 9e0.2x dx

A: We have tofind the indefinite  integrals.

Q: Evaluate the following integrals.

A: Evaluate the following integrals.

Q: Sx(x² – 3)11 dx

A:

Q: /9-x2 dx 2 4. S

A: Given, I=∫129-x2x4dx To Find: The value of I.

Q: r4 dx 7. So

A:

Q: Evaluate the following integrals. 1) La7 dx Ans. 4 1 v1-2x-x2

A:

Q: Evaluate the following integrals (x2 — х)2 dx 1. x3

A: To evaluate: ∫(x2-x)2x3dx

Q: x³ + 1 dx x2 – 4

A:

Q: Evaluate the following integrals. Show all the necessary solutions. ² dx 1.

A:

Q: dx x V1-4 In²x

A:

Q: Evaluate the following integrals. -1 L₁ (3²- (3x² - 4x−¹+2) dx

A:

Q: (x+1)dx x²-3x+5

A:

Q: Evaluate the following integral by using appropriate method. an 3x2 dx x² -25

A: Given:  f(x) =∫3x2x2-25dx                   =3∫x2x2-25dx      By using trignometric substitution Let…

Q: 9. dx V1-x2

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

Q: Evaluate the following integrals using power formula. 1) S3t dt 2) dy 3) S(5x* -8x³ +9x2 - 2x + 10)…

A: We have to evaluate the following integrals using the power formula. 1. ∫3t6dt2. ∫1y3dy3.…

Q: Evaluate the following integral by appropriate method: L, V2 + lx[ dx

A:

Q: Evaluate the following integrals using the tabular method. (i) 2x sin 2x dx

A: We need to evaluate the integral ∫e2xsin(2x)dx by tabular method

Q: Evaluate the following integrals: x2 – x 1. Vx – 1 dx - 1

A: We will find the value of the integral as following.

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: dx 3 Vx Vx (1+Vx)²

A:

Q: 6. Sxe -3* dx хе

A: We solve the above integral using integral by parts which is given in step 2 .

Q: Evaluate the following integrals.

A: ∫x1-9x2 dx Put, 1-9x2=t⇒0-92x=dtdx⇒-18x=dtdx⇒-18x dx=dt⇒x dx=-dt18

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.