Evaluate the following integral 2 I = (4x3 – 3x2 +x – 1)dx, | -1 2.1. analytically 4

Q: Q1 - Evaluate the following integral: J (2x2-3x+2) dx (x-1)2 (x-2)

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Q: Evaluate the following integral: 1 dx, (x² + 6x)/2 x > 0.

A: Indefinite Integration

Q: II. Evaluate the following integrals: 4 1 dx ½2x+ 7 2 1 4. 5. 6. 4-5x -dx-

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

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Q: I. Evaluate the following integrals. Зx3—2х2-4х-3 dx x² (x²+x+1) 2.

A: Given: I=∫3x3-2x2-4x-3x2x2+x+1dx   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: 2x e dx +1 2x

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Q: |(x² + 2x) cos(2x) dx

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Q: 14e" dx 1+ e20

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Q: 1. Find the following integrals. i) S 3e-2x dx 2x2-1 dx ii) S: 2x3-3х

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Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

Q: 5 Find the following indefinite integrals. 10 a. f(x+2)' dx b. J d. [4 (3-&x) dx c. (3x-7) xp-

A: c)

Q: Evaluate the integral. '2 (x - 8|x|) dx -1

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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 integral 1 x3 dx. 1+ x2 0.

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Q: Evaluate the given integral 2x +3 -dx- (x + 1) (x – 1)²

A: Integration formulas help to integrate the given fuction. Simplification of the function helps to…

Q: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

A: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

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: Evaluate the integral. -^x dx e S² sin √1-x² 2

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Q: evaluate the given integral. L (2x - 3/4) dx

A: Solution:Given     Let     I=∫ 2x+34 dxFormula:∫xndx=xn+1n+1+C

Q: 3. Evaluate the following improper integral; -2 2 dx x² – 1

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Q: Evaluate the integral. 4 x - 3 dx X 1

A: Given:

Q: Evaluate the integral. '5 dx L 2- 13/2 (x² – 1)3/2

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Q: Evaluate the following integral. 5 4x-3 -dx x+1 5 ' 4x - 3 | (Type an exact answer.) x+1

A: Given integral is ∫054x-3x+1dx

Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

A:

Q: evaluate the given integral.

A: we have to evaluate the given integral: ∫x2+5x-1x+4dx let the given integral be I. therefore,…

Q: Evaluate the integral. 4(x – 1)² dx x2

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Q: Evaluate the integral 6 dx (x+1) (x2+4)

A: Given,

Q: I need solution to this problem.

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Q: Find the integral below: (x² + 1) dx (2х3 + 6х)

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Q: 4. Evaluate the following integrals. 3 е. X- 2x +2 dx 4x 1

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx…

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Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

Q: Evaluate the integral: 1 2x + 4 dx x² +1/

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Q: 1. Evaluate the integral 2 dx x2 +4x + 20

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Q: Evaluate the following integral. dx 1+ e2x - In 13 ex dx = 2x 1+ - In 13 (Type an exact answer.)

A: ..............(1) take ................put it back in equation 1

Q: 02: Evaluate the following integrals: secxdx 1. S- VIn(secx+tanx) 3. VInn 2xex² cos(e**) dx

A: Use the substitution method to solve these problems.

Q: ex dx V1 - e2x

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Q: 7. Integrate the following indefinite integrals. 3e5x dx 1-2e5x a.

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Q: 3.1 dx x² – 25

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Q: Evaluate the integral. 1 X - 4 dx x2 – 5x + 6

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Q: evaluate the given integral.

A: The given integral ∫2x+1xx2+4dx can be evaluated as, ∫2x+1xx2+4dx=∫2x2+4dx+∫1xx2+4dx The integral…

Q: Evaluate the integral 2∫0(x3−x2)dx.

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Q: How do I find the definite integral of these problems?

A: (a)

Q: 1. Evaluate the following integrals x² + 6x -dx (a) | x³ cot2(x4) cosec² (x*) dx, (b)|Tr3 – 10 – 5x²…

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Q: Consider the integral 3 x2 dx 81- r /2

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Q: 15. Evaluate the integral 10 ·dx (x – 1)(x² + 9)

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Q: 4) Evalvate the integral E 4 1+x² dx

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Q: 3. Find the integral: L,x*dx

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Q: Evaluate the following integrals.

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

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: