4. Compute the following integrals. 2 2x2 + 18 dx. x3 – 3x2 (a) - x3 + x2 + 4 (b) dx. x5 + 8x3 + 16x

Q: Evaluate the following integral.

A: Complete the square of 3 + 2x –x2:

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: 11. Evaluate the following integrals: a) (-3x+1 dx b) S²³+6x-2 x*+6x²

A:

Q: 6) Evaluate the following integrals 4 6)dx J(a*W 3x3-4 dx

A:

Q: Evaluate the integral: √ S - (9x²+7x) (x−1)(x+1)² dx = ← +C

A: Given; I=∫-9x2+7xx-1x+12dx   As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: 12. Evaluate the following integrals: a. S(2x* - Vx3 + x)dx (1-2x)(3+x)(1+x) dr b. fa- 5x

A: 12.a)Given, ∫(2x4-x3+x)dx

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

A:

Q: - Evaluate the following integrals 2e**+11e3x+16e2x -dx e2x+5ex+6

A:

Q: Evaluate the integrals in ∫2y dy/y2 - 25

A: Given integral:

Q: Q2)Evaluate the following integrals in (3) 1- dx 3.x²

A: SOLUTION-

Q: Evaluate the integral. In3 3e2x dx In3 3e 2x dx = 0

A: As we know that; ∫a·fxdx=a·∫fxdx And ∫eaxdx=eaxa+C From the given problem: I=∫0ln33e2xdx

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

A:

Q: 3: Evaluate the following integrals: (2) 4*+23x - dx 2x

A:

Q: Evaluate the following integrals 5z (5 – z°)*dx A. 3 -dr 3 В. 6x + 5 c. /"zV9-z'dz С. 1 -dr 5 - edz…

A: Answer and explanation is given below...

Q: 3. Compute the following integrals. 2/5 (a) V4 – 25x² dx.

A:

Q: Find the integral. J 3 x√9 - (In x)² + C dx

A:

Q: 1 Evaluate the following integral. dx X4V9-x2

A: ∫vn dv = vn+1n+1+C

Q: Calculate the following integrals: (6X-5)dx 3.1 I = S V3x²-5x+6

A:

Q: Evaluate the following sum of iterated double integrals: -2у 2 •4–2y dr dy + | dx dy 0.

A:

Q: Evaluate the integral fe (2x+4) (x² + 4x + 2) dx n- by making the substitution u = x²+ 4x +2.

A: In the question we have to find the integral of the given function.

Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: Compute the following integrals: 1 + 4) x 2x+4)x + 4x2 +x 1. dx e+2

A: We use substitution method

Q: 7. Evaluate the following integrals. 5x* (a) S ++ sec²x)dx 5x2 (b) S xv7x2 + 12 dx (x + 5) (c) S dx…

A:

Q: 4. Calculate the following integrals: 4 3 dx 1 – x2 dz 25z2 + 1

A:

Q: 10.) Find the integral of* 3 (-4y ) ( +14y-7) dy

A: We need to evaluate ∫3y6-4y-3y7+14y-2-76dy                          (1) Let y7+14y-2-7 = t On…

Q: 3. Evaluate the integrals. dx ( Use u = Vx(1+x)

A:

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

A:

Q: Evaluate the integral: Se³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

A:

Q: Evaluate the integral. | (In(3.x))² dx = +C

A: From the given problem: I=∫ln3x2dx  ....(1) Let, t=3x So, ddxt=ddx3xdtdx=3dx=13dt Nw substitute…

Q: 4. Evaluate the improper integral. dx х2 — 1

A: Consider the given integral as Solving the integral

Q: Evaluate the integral.

A: We have to evaluate the integral: ∫x3xx2+3y2dy Here we have to integrate with respect to y so x2…

Q: (3) Evaluate the iterated integral , " (3 + x² +v²) dx dy.

A: First integrating with respect to x and then with y

Q: Which of the following integrals does not require substitution? o fxsin(1 – x²)dx dx 5x²/2 + x3 •…

A:

Q: Evaluate the integral (x – 1)ez xp- x² – 2x + 2

A: The objective is to find ∫-∞∞(x-1)eix(x2-2x+2)dx It is known that, eix is an increasing function.…

Q: 1 . Evaluate the integral: S, S (4x³ + 6xy - 3y²) dx dy -1

A:

Q: 4. Evaluate the following integrals: (a) S (2x³ – x² + 3) dx - (b) S x*Vx5 – 1 dx S ds (c) S V2s+3

A:

Q: 9. dx V1-x2

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

Q: 4. Determine the following indefinite integrals: a) S(2x* + 3x³3 – 7x² + x – 5) dx b) S(x – 5)² dx •…

A: 4. Power rule of integration states that: ∫xndx=xn+1n+1 (a)To evaluate the integral:…

Q: In Evaluate the integral: Sé e x²+3x-7 x-2 dx

A: Option (b) x22+5x+3ln|x-2|+C

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: S √x²-a² X dx

A: To solve the given integral.

Q: 9. In evaluating the improper integral dx , which of the following is true? (1-3x)2

A:

Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

A: The given integral ∫2xx2+410dx

Q: 2. a) Evalute the following improper integrals dx Vx – 3

A: We will solve the problem.

Q: Evaluate the improper integral s dx -2 (2+1)4/3

A: Given: To evaluate ∫-201(x+1)43dx

Q: Evaluate the following integrals: 1) 3x(x-5)dx 2) l dx o x-1 9 dy 3) +2} -s dw 4) -3 w+1 5) xáx (…

A: 8) Consider the integral: I=∫-293dyy-35

Q: S 3x+1 - dx x²-x-6

A: Given integral is  I=∫3x+1x2-x-6dx