EXERCISE 3 (INTEGRATION BY RATIONAL 1. Please answer the following questions. 2x +1 dx a)| x(x² +1) .2 b) 4x°-8x2 -5x+5 2x-1 dx 3 4x -8x c) dx 12 x++4) 2x -x2 +4 d) 关 dx .3 .2

Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

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Q: Determine the integral of the ff. functions. 1. S - 10 sin 5x dx 2. S 4 x cos x² dx 3. S sec 2 (3x +…

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Q: Evaluate the integral. V3/2 5x2 dx V1 - x2

A: Consider the trigonometric identities 1)  cos2x = cos2x - sin2x = 1- 2sin2x 2)  cos2x + sin2x = 1 3)…

Q: Evaluate the integral dx (3x + 15)²’ by making the appropriate substitution: u = dx + 15)?

A: To evaluate:∫dx3x+152

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

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Q: Exercises (4.8) Evaluate the following integrals (1) ſ sin3x sin2xdx (2) S sin3x cos2x dx (3) […

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Q: Exercises (14): Evaluate the following integrals 1. dx 2x- x2 2. dx V4x2 – 3

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Q: 1 x+1 Integrate: r21?

A: Here we have, I=∫01x+1x2+2x2dx

Q: S 6x®cos (x³) dx „8, ,3•

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Q: In Exercises 1–8, decide whether the integral is improper. Explain your reasoning. dx dx 1. 5х — 3 -…

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Q: Evaluate the integral. V3/2 19x2 dx V1 - x2

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Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: How do you solve problem 29 using U-sub?

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Q: Evaluate the integral. dx 4 a > 0 (a² + x²)3/2?

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Q: Integrate the function. 16x +즐 + C V16 -2 8 sin 1 +C 2 V16-2 +C + 16V16 - x2 8x - W16-2 +C

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Q: part C

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Q: 3 Evaluate the integral: dx 2 Vx -1

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Q: Find a suitable method for integration of Sin (x²) x = 0,√ using a two-point sample of Sin (x²) x =…

A: We have to find the integration I=∫0πsinx2dx let f(x)=sinx2 For ∫abf(x)dx, two point formula is…

Q: a) For 0 ≤ x ≤ 1, show that < x². √2 + x b) Use the estimate in a) and integrate it to prove that…

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Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

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Q: 9. Evaluate the integral ex V2e-2x – 3e2x 2/2e-2x – 3e2x +C А. 1 3eªx – 2+C B. 2/3 Arcan V3e2x…

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Q: A b B d a The integral 15x²x³43x - 19 (x + 1)²(x² - 6x +13) can be rewritten as Ax + B D C + ax² +…

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Q: Use the tabular method to evaluate the integral |(* + 2x – 1) cos(4x)dx

A: Given:∫(x3+2x-1)cos(4x)dx

Q: Show that 3x2 +6x +2 = 3 (x+1) - by completing the square. Hence, evaluate the 2 integral dx. V3x? +…

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Q: 1. Evaluate the integrals (a) fxsin 2xdx, (b) f(3x - 1) eª dx, Hint: Use the Integration by Parts. 3…

A: SOLUTION-

Q: 1) Evaluate the integrals: (a) f sin³ (2x) cos (2x) dx (b) sin³ (2x) cos (2x) dx

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Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

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Q: 7. Use integration by parts to prove that for any positive integer n, | cos"x dx = 1 cosn-1xx+ n - 1…

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Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

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Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

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Q: Evaluate the integral. dx xVx2 -6 sec" 13 x| +C O sec" 13x - 6| - C sec +C 6. sin 3 x+c 6.

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Q: You are told that Lif(x) dx = 9 and /, 8(x ) dx = -2. what is the %3D value of the definite integral…

A: To Determine: what is the value of the definite integral∫-173fx-4gxdx Given: we have ∫-17fxdx=9 and…

Q: Evaluate: (2x + 1)3 dx by two methods: 11) let u = 2x + 1 %3D 12) Expand (2x + 1)³ Compare the…

A: Integration

Q: 7. Use integration by parts to prove that for any positive integer n, п - 1 Scos | cos"x dx = 1…

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Q: Evaluate the integral dx (2x + 6) by making the appropriate substitution: u = dx (2a + 6)°

A: To evaluate the given integral.

Q: The approximation of the integral f(x-1) cos(x+2) dx using two points Gaussian quadrature formula…

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Q: 3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx…

A: We have to evaluate the integrals.

Q: 2. Use symmetry to evaluate the given integrals. -200 A) S, 2x5 dx -200 В) cos х -п/4 B) S"/ cOS x…

A: A) ∫-2002002x5 dxB) ∫-π4π4 cos x dx

Q: Evaluate the integral dx (2x + 4)* by making the appropriate substitution: u = dx (2x + 4)°

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Q: Find the integration inner product on C[-4, 3] of the given functions. f(x) = 16x g(x) = 2x?

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Q: Step by step

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Q: Evaluate the integral. 6x2 sin AX dx Step 1 To use the integration-by-parts formula u dy = uvV – v…

A: Given:

Q: Evaluate using Integration by parts. J cos 2x sin 3x dx cos 2x cos 3x - sin 2x sin 3x + C None of…

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Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

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Q: 10х> — 5х For the integral -dx , if u = x*-x2+6 then Mdu = (10x³-5x)dx, what is %3D x4-x²+6 M?

A: We have integral ∫10x3-5xx4-x2+6dxifu=x4-x2+6

Q: Evaluate the Double Integral. 4 V16-x2 b. 2x dy dx

A: We have to evaluate

Q: 1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

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