Evaluate the given definite integral. -2 . Jx(3-x²)*dx -3 -2 S2x(3-x)°d dx = (Type an integer or a simplified fraction.) -3

Q: Which among the following is an improper integral? -0.5 dx a. O5- -0.5 1-x2 csc?x b. Si dx V5-csc2x…

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Q: 1. Solve the following integral by using the Integration by Parts. (a) x sin x dx (b) e 2x sin 2x dx

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Q: Q3: Find the integral for the following functions: - 6 dx 1) 2 x+2

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Q: Q1: Evaluate the following integrals by substitution dx 1. e cos e*dx dx 3. J 2x- 3

A: Solve by substitutions

Q: 2. Find a) ³ dx b) xdx. Hence, find whether the following integrals exist and, if they do, find…

A: To evaluate the given improper integrals

Q: 4. Determine the following integrals 4.3 (a? + x*)cos(2x) dx

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Q: 1. Evaluate the following integrals using appropriate methods and simplify your answers. (a) x*e* dx

A: To Determine :-  The given integral is : (a) ∫ x3 ex2 dx

Q: 1/6 dx 3.S T1-9x2

A: Solve the definite intregal

Q: Find the indefinite integral.

A: Let ex+e-x=v. Differentiate both sides: (ex-e-x)dx=dv Substitute v and dv in the integral…

Q: evaluate the given integral.

A: Use Substitution method to determine the value of  integral .

Q: I. Evaluate the following integrals. •ln 2 #3. e2" sec-(e")dx

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Q: -3 2e4 Evaluate the given integral: Jo 1+e2x dx.

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Q: Q4: Solve the following integrals:- dx 4dx (1) S: (2) S: sec xesin x (3) S x sec? x dx 2+cos x

A: Note:-  As per our guidelines, we can answer the first three sub-parts of this problem. For the…

Q: Calculate the definite integrals (a) I₁ =¹7 (2x − 1)(x + 2) dx - 18 (b) I₂ =2₂¹8 (x + 2)(√√x - 2) dx

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Q: Q2 Find the integral for the following : dx 1 1-5 2- fe-*sec? (ne-*)dx 3- S dx 2vx+2x 1+e*

A: We have to find the Integral for given expressions. 1. ∫dx/(2√x + 2x)  2. ∫e-x sec2(πe-x)dx  3.…

Q: Q2) Evaluate the integral x dx a -0.

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Q: 24. ( (x² + 1)e*dx

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Q: 2. Evaluate the following integrals. 6 a) dx x² – 3x b) | 4.2? cos(x³ + 2) dæ 4x2 c) / 4x² ln x dx

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Q: Q1) A-Evaluate the following integrals: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x-2.…

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Q: 2. Calculate each of the following indefinite integrals: а. b. dx e* +1 dx: Vx' -1 In x dx С. d. 5x…

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Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

A:

Q: 5x+6 Consider the indefinite integral e+0 dx:

A: given equation= e5x+6

Q: 2 Evaluate the definite integral S: 1 dx. 1 x+a2 ter -17 a- 19

A: solution:

Q: 1. Evaluate the following integrals. Show all steps! 2 x + 3 dx x(x – 3) 1? — 4x + 6 - dx (b) | (x –…

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Q: Q4: Solve the following integrals:- dx 4dx dx (1) S: (2) S sec xesin x (3) S x sec? x dx (4) S -…

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Q: Find the indicated integral (if it exists) / e bx dx e12z +1

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Q: 3. Evaluate the definite integral. Give exact answers S(x² + 2x – 4)dx - a. ~2 2x+1 dx Vx2+x-2 b.

A: Take integration. Follow step 2nd .

Q: Q4: Solve the following integrals:- dx (1) ſ; 4dx (2) S; (3) ſ x sec² x dx 2+cos x sec xesin x

A: Since you have posted multiple subparts question in this question so i have solved first three parts…

Q: Q3: Find the integral for the following functions: - 1) 2 6 dx 2 x+2 2) S 3co t(x). csc²(x) dx 3)…

A: To find the given integral.

Q: (d) (x² + 1)² dx (e) L dx (x² + 1)² (f) eir dx

A: d. Given

Q: b) S x² Sin(x") dx 3

A: Given, ∫x3sinx4dx  We have to determine this integral .

Q: 3. Evaluate (using appropriate substitutions if necessary) the following definite Integrals. (a) ,…

A:

Q: find the indefinite integrals. 1. ∫ e−0.05t dt 2. ∫ (3/t  -  2/t^2)  dt

A: case 1:The given indefinite  integral  is ∫e-0.05t dt.Let u = - 0.05t, then du/dt = -0.05.

Q: Q2) Evaluate the integral x3 dx 3 a *0.

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Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

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Q: -2 Evaluate the definite integral S: 1 dx. 1 x+a²

A: general answer is Ln|(2+a^2)÷(1+a^2)| Where a = -3/5 Final answer is Ln|59/34|

Q: 1 dx x² +1 e +

A: solution:-∫02ex+1x2+1dx=∫02exdx+∫021x2+1dx=ex02+tan-1x02=e2-e0+tan-12-tan-10=e2-1+tan-12     Ans

Q: dx S. 2x - 1 e

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Q: (а) 4x³ dx -2 (b) | (2г° — Зг + 6) de (c) | (2г — Зг + 6) de

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Q: Q(1) Find the integral of Vx² – 16 dx

A: Use substitution method to find its integration.

Q: Find the indefinite integral x2e +e² dx.

A: The given indefinite integral is: I=∫x2e+ex dx

Q: 1+e* dx X- e-t

A:

Q: (ii) Find the following indefinite integrals: 1 (a) dx (b) dx 5 - x* xe* ! dx (c)

A: A)I=∫ 1x3+1x3 dxI=∫ x-3 dx + ∫ x-13 dxI=x-3+1-3+1 +x-13+1-13+1 +CI=-12x2+3 x232 +CI=32x23 -12x2+C

Q: Evaluate the definite integral. *2 e 1/x* dx J1 +s

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Q: Q2 Find the integral for the following : dx 1-S 2Vx+2x 2- Se-*sec² (ne¯*)dx 3- S dx 1+e*

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Q: 3 Evaluate the definite integral dx. (x- 5)4 -2

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Q: (3) Evaluate the following indefinite and definite integrals: (a) ſ(x³ +e* )dx (b) 1 |dx + XVx -1 2…

A: We will evaluate the given integrals as shown below

Q: aluate the definite integral. x6 + a2 dx (a > 0)

A: We have to find the integral

Q: 1. Find the general indefinite integral or evaluate the definite integral, as necessary. dx b) S,…

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Q: A. Evaluate the following integrals 1. 2. L. 3. , e*dx dx dx -1 x2/3 4. SE tanodo -4 dx

A: solution:-Q.(4) ∫-∞π2tanθdθsolving the improper…