2 t X Vx2 + 4 2 - 4 - dx 3. =2 X 4-30 Evaluate the integral. dx 9-x 4. x- 1 dx 5. x dx a > 0 7. Jo (a2+x2)/2 + x

Q: 2. xy dx dy

A: While integrating wrt 'x' we will keep 'y' as constant. While integrating wrt 'y' we will keep 'x'…

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

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Q: - 23 L f(2)dx = 11 - 82 and - 23 L g(z)dæ = 30 82 and – 23 h(x)dx = 25 - 82 | what does the…

A: Given ∫-82-23Fxdx=1 -1          ∫-82-23gxdx=30-2          ∫-82-23hxdx=25-3We find…

Q: Find the indefinite integral. 1 dx 3 (x²+9) 2 a. b. C. d. x² 9√x²+9 +C +C 9√√x² +9 x 9√√x² +9 x² +C…

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Q: Find the integral | 2(x* – x°)(x5 – 1)®dx а. b. In x2 dx 2х J x + 3)* С. 5.

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Q: 1. f(x_y)= VG-x² -y? and find double integral..

A: Double integration

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A: We use partial fraction decomposition.

Q: 9. dx Evaluate the integral| - 3 x( In x) 3 9. dx 3 x( In x) 3 II

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Q: -3.5 x/(16 – x²)3 dx 0.5 Find the numerical value of the integral using: a.) Trapezoidal Rule (n =…

A: Given: ∫3.50.5x16-x23dx To find: Numerical value using trapezoidal rule.

Q: 5 1 So (125 + 25x + 6) dx 6o S X (1 + x²)3 dx / 1 + x² dx 1

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Q: Evaluate the integral. 4 f(x) dx   −2  where f(x) =    2 if  −2 ≤ x ≤ 0 3 − x2     if  0 < x ≤ 4

A: Definite integration

Q: Q2) - Evaluate the integrals: V16-x 2. 3. SA dx 4. S Vx2 +1 dx dx

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Q: Q I find integrals 3-2X 2 +4X dx

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Q: Evaluate the integrals: x² dx (x-1)(x²+2x+1) -dx 1. S 2. S x²+2x x4-3x²-4

A: Here we have to find the integral.

Q: Double integral of x^3 cos(x^2y) dxdy ? for x=1/y, x=1/2 & 1<y<2

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Q: (6x³ + 3x? x² – 16 89x – 52 dx Consider the indefinite integral Then the integrand decomposes into…

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Q: Q3) Reverse the order of integration and evaluate the integral 8 2 dy dx y2 +1

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Q: Find the indefinite integral. 1. 16 + t² dt * (x² + 4)³/2 + 4)3/2 2. -dx-

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Can you help with this problem step by step?

A: We need to compute the given integral.

Q: valuate the integral. (Use C for the constant of integration.) dx 3/2 (ax)² – b2]

A:

Q: 19. Evaluate the integral Z √(x^2 − 9) / x^3 dx

A: firstly divide the numerator by denominator part by part to simplify the integration

Q: 3. S? dx ( Improper Integral) (х-2)5

A: The given improper integral is: ∫13dx(x-2)23 Since the integrand f(x)=1(x-2)23 is undefined at x =2…

Q: 1 x 5xy dy dx 0 x2 ate the double integral.

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Q: Find the antiderivative of dx / (25 + 4 x^2) * O (1/2) arctan (x/5) + C O (1/10) arctan (2x/5) + C O…

A: An antiderivative is an integral process that can help a function to get back into its parent…

Q: 2. Use the substitution u = x² and then Integration by Parts to evaluate / x³e**dx.

A: Given: ∫x3ex2 dx We substitute u=x2, that implies du=2x dx. By using this substitution, ∫x3ex2…

Q: Q1/ Evaluate the integral: -За (2уах 3a dy dx x2 4a by changing the order of integration.

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Q: Compute for the general antiderivatives of the functions 1. S(x – 2)? dx 2. S(2x + 3)³ dx 3. [ sin…

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Q: 9. Use integration by parts to show that pP+1 ]n°(x) |aP In°(x) dx p+1 p+1

A:

Q: Q1 / Evaluate 3 only of the following integrals: 1) S 3x² dx 2) S ( +x) dx 1 3) S(2t + t=1)² dt x+3…

A: For a function g(x) with f(x) as its derivative, i.e; Then ;

Q: 6) Evaluate the improper integrals ∞ 5 a) 5² (+ + e-") dx s (-x) е 2 7 5 b) ² = 8 dx 4x-8 2

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Q: Evaluate the integral: 1. - 1 (1- 5x + x³ – 2x5 5х + x3 — 2x5 dx x2 2. S(y³ – 3,/y+ Vy) dy

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Q: -3 2. (2x+4)3 8x dX use integration by parts and then find the value of definite integral.

A: A detailed solution is given below.

Q: 5. Evaluate the integral. 1 -dx æ² – 1 a) b) S. +4 -dx x² + 4

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Q: (j) S 3r2+5 dr (k) S(x+ 3)(x +1)*dx (1) S x In(x)dx

A: Note the results : Power rule :                  ∫xn dx=xn+1n+1+C ; n≠-1 Integration by parts…

Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: Q/Evalute the integrals Vin3 dx dy 973 3. サーメ 2) dz dy dx 1 1-x 1 3.

A:

Q: can you please help

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Q: 2. Evaluate the integral. -2 (a) (x² – 3x) dx - -1 •3 (b) Lce L(e + 2)(t – 3) dt -2 (c) 2.9 x° dx

A:

Q: Q: Find the integral for the following functions: - 6 dx 1)2 x+2 2) fe x. In(x) dx 1 3) S: dx…

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Q: 02:- By using integration by part, find :- (Choose two only) 1- Sxe-* dx 3-S(1+ x²)e¬*dx 2-f Inx…

A: As per the company guideline's we are supposed to answer first question as mentioned by the…

Q: Find the integral. √(x + 1)e 6x² + 12 е 12x dx √(x + 1)e 6x² + 12x dx = [

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Q: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: ー2X 2 e Evaluate the integral 4え |

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Q: Find the general indefinite integral: 1) S(x13 + 7x².5)dx 2) S Vx5 dx 3) Sv(v² + 2)²dv 4) Sx³cos(x*…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: One of the correct steps to evaluate x2inx x²Inx dx to yield the correct integral A x?Inx B 1 x3 dx…

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Q: II. Evaluate the following integrals: x- 2 1. J- -dx +1 2. J; -dx 8х + 3 3. J- x -4x-9

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Q: Find the integral. 5x* dx (5+x*)* 1 O A. 3(5+x)3 OA. 1 О в. В. +C 5(5+x*)5 Oc. (5+x)°. +C

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Q: y Evaluate the integral -dx using х3 — х? — 4х +4 X-1 x +2 x - 2 Зx? — 2х — 4 dx = J x – x² – 4x +4…

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Q: 5. Find the integral | 2(x* - x°) (x5 – 1)®dx x In(x + 2) dx а. d. | In x? dx | 2xe** dx b. е. 1 2x…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.