3 The value of (Isi n(x)| + x²) dx is .a 2 f(- sin(x) + x²) dx 0 .b .C 2 f(sin(x) + x²) dx -3 .d 3 , (sin(x) + x²) dx

Q: 4. e2x sin e*d x, use algebraic substitution

A: Given :  Intergral ( e2x sinex dx)

Q: sin x – x dx = ? X (a) E(-1)"- 22n (b) E(-1)". 22n+2 (2n).(2n)! (2n +2).(2n +2)! n=l n=1 22n+1 (2n…

A: We have, ∫02sinx-xxdx   It is known that, sinx =x-x33!+x55!-x77!+...

Q: Sco The value of cos (x+3) dx with U=x+3 is -cos (x+3) sin(x+3) +C -cos(x)+c

A: The given integral is ∫cosx+3dx.

Q: Evaluate the definite integral

A: Now let us consider,

Q: 5 dx Find dx, x> V25x? -9 5x In 25x2-9 + C 3. sin-13x+c 1+9x2 +3x|+c 1 V1+9x? + C 3x 3. + C V25x2 -9…

A: The solution is given below in the next step:

Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

A:

Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: SIn(x + 12)dx = O A. (x+12)In(x+12)23-23x +C B. (x+12) In(x+ 12)- 23x +C OCxIn(x+ 12) -x+ C 23 23 +C…

A: We will use integration by parts to solve this

Q: sin x – x dx = ? X 22n (a) E(-1)". 22n+2 (b) E(-1)". (2n).(2n)! (2n +2).(2n+2)! n=1 n=1 22n+1 22n-1…

A:

Q: r 3n 4 Evaluate sin'x · cos'x dx 5. n /2

A:

Q: In x2/25+ x² dx , we let x= 5sine. T True F False

A:

Q: S sin(1 – x) (2 – cos(1 – x))* dx A (2-sin(1-x)5 (2-sin(1-x)5 +C +C D (2-cos(1–x)5 +C (2-cos(1–x)5 +…

A:

Q: sin x - X dx = ? (a) (-1)". 22n (b) (-1)". 22n+2 ( 2n).(2n)! (2n+2).(2n +2)! n=1 n=l 22n+1…

A: ∫02sin x-xxdx

Q: 2х —1 The value of| dx is 1+x-x, tan А. 1 В. О С. 1 D. 4

A:

Q: f1(x) = sin(x1) cos(x2), T f2(x, y) = xy, f3(x) = xx¹, € R² x = x, yern XER"

A: Given the following functions                  f1(x)=sin(x1)cos(x2),   x∈ℝ2f2(x, y)=xTy,   x, y∈ℝn…

Q: ecot x 20. J sin² x(e- cotx) ax is equal to A. ecot x 1 + C ecot x C. -ecot x + C D. –ecot x + C

A: Given problem:-

Q: S sin 7x dx is equivalent to which expression? A S(1– cos²7x)(cos 7x) dx B. S(1 - cos'7x)(sin 7x) dx…

A: As per Bartleby guidelines we're supported to answer only one question when two or more different…

Q: -(sin³(x) + sin (x³) ) dx A 3sin'x + cos (x³) B 3sin?rcos(x³) + 3xr?cos(x³) © 3sin?x + cos (3x²) D…

A:

Q: f (x) = xe-* – sin?x Newton Raphson (1st Method) @ x1 = 0.5 Newton Raphson (2nd Method)@ x1 = 0.5…

A: Newton Raphson Method:- Hence by Newton Raphson Method Root of the equation is 0.61447 (correct…

Q: The value of A.cos(x²+)+C cos (x² + + C fx sin (x²+3) de dx B. - cos (x² + 5) + C D. -cos (x²+)+C

A: Option (B)

Q: S²(x²-4x² + 324 232) sin(x) 4x⁹ (1+x²)² A) True B) False |dx=0

A: ∫-11x7-4x9+sinx1+x22dx

Q: (a) S(7 – sin(x) + 9cos(x))dx - 1 (b) S (e* + 3* – - 2 V1-x

A:

Q: 6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

A:

Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: 3. 4. 5. π X dx sin() co₂ (:) ª 2x - 1 4x1 dx 8. 9. (x-1) √x dx _2_2x dx 10. S√₁-2² a x dx

A:

Q: X 1 -x sin(x)×e 50 dx 4

A: Let I=∫14sinx ex50dx. We will evaluate this integral using integration by parts. ∫udv=uv-∫vdu. We…

Q: d3 (2 sin x + 3 cos x Find dx3 x³).

A: Given that: d3dx3(2sinx+3cosx-x3)

Q: For S* sin x dx, what is dv? sin x dx OA 2x dx - cos x+ 2x sin x+2 cosx+C O.

A:

Q: x + 3 Q10: Evaluate dx. 5 + 4x — х2 5 sin¬' (*) | + V5 + 4x – x² + C 3 -5 sin-1 (x 3 -)- V5 + 4x –…

A:

Q: V.P. [ -8 COS X (a²-x²) -dx, (a> 0).

A:

Q: e* sin(e^)ax 8+cos²(e*) (x+2)dx x2-3x+5 .2 dx

A: Given that

Q: * (s in-(x))² dx = V1-x2 Select one: а. sin-(x) + C 1 - x? b. (sin-(x))³ + C 3 C. sin-V1 - x²) +C O…

A: With the help of substitution method, integration is solved.

Q: 2 a) ; 1 :+ 5e* dx =? sin? x 1- x2 b) (x² – x + 2)* (2x – 1) dx =? sin 2x c) 5 + sin² x dx =?

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: cos √x+1 O Σ n=2 (-1)"x²" (2n)! n+1 x² Σ nal

A: I have given the answer in the next step. Hope you understand that

Q: 6. The value of A. sin ¹¹x + √1 + x² + C B. sin-¹ x - √1 + x² +C C. sin-¹ x + √√1- x² +C D. sin…

A:

Q: x2 Q1 (x sin x+cos x) -dx

A: For integrating the given integral we will use the below-mentioned integration formulas…

Q: 1. (6x + f²)dx + f(2x – 3f)df = 0 2. (cos2f – 3x²f?)dx = (-cos2f + 2x sin2f + 2x³f)df 3. (fe*f –…

A:

Q: P2: |(e* sin x + x In x) dx

A:

Q: Using appropriate substitution dx 4 (x+ 1)2 - is equal to -/4-(x+1)2 – sin- (*) + C the above…

A: Given problem:-

Q: Evaluate D³(sinx - 4e²x) (A) sin x-32e²x (B) -cos x-32e²x C -sin x-32e²x D cos x-32e²x

A: Finding the third derivative of the function

Q: sin x – x dx = ? %3D 22n (a) E(-1)". 22n+2 (2n + 2).(2n+ 2)! (2n).(2n)! (b) E(-1)"- n=1 n=1 22n+1…

A: ∫02sin x-xxdx

Q: [²(x². x7-4x⁹+ (A) True B) False sin(x) (1+x²)² dx=0

A: The given integral is ∫-11x7-4x9+sinx1+x22dx. We have to evaluate the given integral.

Q: 2 S tan x sec x dx e-0.3x =27 Q5) (A) Evaluate (B) Solve for x: |3D

A:

Q: 3n 2n n S " S"(sin x + cos y)e? dx dy dz 2n 'n A. 2n(e2n + e3™) в. 2п(е2т — езт) c. 2n(e3™ + e2") D.…

A: Given: I=∫2π3π∫π2π∫0πsinx+cosyezdxdydz   We know that; ∫sinxdx=-cosx+C∫cosxdx=sinx+C∫exdx=ex+C And…

Q: 8. The value of ve A. sin-1 (e) + C C. sin-1 (e-x) + C dx B. -sin-1 (e-2x) + C D. sin-1 (e-2x) + C

A: Topic = Integration Correct option = A

Q: g(x) = 2 – sin x 5m/2 2m 3m2 2 m2 3m12 5m/2 f(x) = sin x

A: For a function g(x) to be greater than or equal to some function f(x), the graph of g(x) must always…

Q: sin x - x dx ? %3D 22n (a) (-1)" (b) (-1)". 22n+2 (2n + 2).(2n + 2)! (2n).(2n)! n=l n=1 00 22n+1…

A: Consider the given information: To evaluate the integral ∫02sinx-xxdx