2 4 dx J x/3(1+x²/3) 3 gin

Q: 31 -1 dx 7х — 6 -

A:

Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

A:

Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

A:

Q: 4 dx. x'V16-x (c) By using x= 4sin (0), find

A: We have to find integration by substitution

Q: E) INTEGRAL : 9.) S(5t3 + 2t? – 5t – 50)dt 10.) S(3x2 + 2x + 500)dx

A:

Q: By Simpson's method, find an approximation for [(x³−2x³)dx_(n=4) 0

A: What is Simpson's Rule: Simpson's rule is a tool to approximate an integral. It is the process to…

Q: 30. 5e dx 31. dx Зи du - 1 33. 3. x² dx 35. (x' + 5)* 37. ((3 In z + 2)4 39 dz

A: We have to solve the integration

Q: 14. Evaluate the integral 2 ·dx 2x2 + 3x + 1

A:

Q: 2dx J x (3(ln x)2 + 12 In x – 15)

A: The given integral can be evaluated using the factorization and substitution technique.

Q: 3 tan-(x)dx O V3 - In (8) V3 TL In (4) 2/3 2.

A:

Q: 2FI 2 sin nx dx cos nx dx =0, where n integer. %3D !! 0.

A: Note: -     as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 2dx J = (3(ln x)² + 12 In x – 15)i -

A:

Q: 5. 12 sec² (3x) dx 0.

A: We have to solve

Q: / (6x" – 7Va+ 19x- 8 -- + Evaluate + 14e0* + V11 dx. (You don't have to show the work.)

A:

Q: 4 (1+2 In x)* 6. J dx б.

A: We have to find

Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

A:

Q: 1 (7 – x²) sin nxdx An 2(-1)"+1 n3 II

A: Integration by parts  ∫U·Vdx =U·∫V dx-∫dUdx∫V dxdx Where U and V are the function of x . Also,…

Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: 1. S Vcos 20 sin 20 d0 x²-x 2. S- dp- (x+1)

A: To  evaluate the integral.

Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

A:

Q: Evaluate the definite integral. "1/3 3 dx V1- 9x²

A:

Q: (y5 – x²e») dx dy -11-3

A:

Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: 10. J(3x3 — 5х + sin3x) dx -

A:

Q: 3 dx V16-x²

A:

Q: integrate (2 + x^2)/x^1/2 dx from 1 to 4

A: to find I=∫142+x2xdx

Q: 3 sinº x dx 4 Show that

A:

Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: Integral of 2cos^2x+3sin^2x dx from 0 to pi/2

A:

Q: 1 .2 2 dx = 0 xe 0- -

A: Given: 12π∫-∞∞xe-x22dx=0   We know that; ∫eax+bdx=eax+ba+C     Note: As per Bartleby guidelines we…

Q: Su+1 dn th-2

A: I =   ∫135x + 1x2 + x - 2dx    = ∫135x + 1x2 + x - 2dxWriting5x + 1  = A (2x + 1) +BOn solving , A…

Q: Find the value of the definite integral: 4x dx -2

A: ∫-254x3 dx

Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: find the most general antiderivative of f(x)= 2x^3 - sinx + 4e^x

A: We find the integral of f(x)= 2x^3 - sinx + 4e^x We separate the integral first.

Q: q² In(x³ + 1) dx

A:

Q: Integrate ing with res pect to x; +8 - (3x+2) - the followi Sin (x) + + 2 4x dx 4 5x

A: Formula : 1. ∫xndx=xn+1n+1, n≠12.∫(ax+b)ndx=(ax+b)n+1a(n+1)3.∫1xdx=lnx4.∫sinx…

Q: Evaluate the integral. 1/2 3 sin 2nx dx 2.3 16 16 3 8

A:

Q: Find the indefinite integral

A: Consider the integral: I=∫sec42x5dx……1

Q: Evaluate 4 dx V4-x2

A: To find out the integration.

Q: Use Euler's method (with all details) to find approximate value of = 2y - 2x² -3, given that y = 2…

A: Given: y'=2y-2x2-3 , y(0)=2 , h=0.3. We find y(3) by using Euler's method. The formula for Euler's…

Q: Find the definite integral 10 (2х — 3) dx

A:

Q: 2. Solve the ODE using Separation of Variables. dy dx 5x²+4 y+1

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Q: 3メーメヤxー9 dx x²-3x+2

A:

Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

A:

Q: dx 4. S x²Vx2-9

A: 4). Given: I=∫dxx2x2-9   ....(1)   As we know from the trigonometric identities; 1). cosx=1secx 2).…

Q: 4x2-3 f (x) 2х3+x2+7

A:

Q: 1. Use integration by parts to find (3x – 1) sin x dx.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…