f(x)dx3D0 and f(x)dx = 11 evaluate 3f(x)dx - Given A None of the given Choices 55 B 3 11 D 5 11 E 6

Q: 2x3 + 11a? + x +9 x + 2 Given x2 +1 (2a3+ 11a2 + x+ 9 dx Evaluate (Don't forget to include the %3D…

A: use substitution method for solving the integral

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Q: 4. (x² + b²)dy = 2x[(x² + b²)² + 3y]dx; y(b) = 4b*; b is a constant # 0 %3D

A: Linear differential equation

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A: Simplify the given differentiatial equation to obtain the expression of dydx.…

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Q: Evaluate: e-2x dx 1 1 1 1 a. c. -2 - e2 d. 2- 2e? 2 2e2 b.

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Q: Q2) Solve the D.E dy + (xy-xy2)dx 0 %3D

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Q: 2x²+2x +1 Evaluate: e x+1 dx. x2 A *+ In|x + 1|+C 1 +C x+1 B X+ None of the given choices…

A: Integral calculus is the fundamental discovery was the link that exists between this and the…

Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x + 13) Ax + B What is the value of dx ? ax²+bx+c 31 -…

A: Given integral ∫15x2-x3-43x-19(x+1)2(x2-6x+13)

Q: f (x) = [x + 4] df 1 =? dx 8 - O A) 1 В) 10 о с) -1 D) 2 O E) 0

A: The function f(x)=x+4. We have to find dfdx12=?

Q: d²y -6空+9= 0. dx2 dx 业

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Q: d*y d?y Find the complet solution for the ODE dx4 = x² – e-* + 4x – 5 dx?

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Q: Question d²y Find if-x2 + 3y² = 4. dx2 Provide your answer below:

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Q: Q5:A/ Find In x dx XVIN? x + 1

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Q: S₁ A B If 2x²+x-2 (x+1)(x²+1) ² 1 -- 2 U NIG 5 —— D E) None + -S₂ -dx = A x + 1 + B (2x) + C x²+1…

A: Partial fraction decomposition

Q: Find the value of E 2) Evaluate y dx 3) x e

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Q: f(x) %3D e 3.

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Q: Solve the D.E x dy+ (2y-x-11dメ-0 (24-X-1)dxメ= 0 %3D

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Q: Solve the equation of change df/dx = 3 if the initial value of f is 7. a. f = 4x + 8 b. f = 3x + 7…

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Q: 20 (i) E(13)* k=0 (ii) fºx'e-2= dx (iii) [ e-(z-13)²/8 dr

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Q: S Ve3x dx A 2 X- e3 2. C + C ez* + C - 1 e3x + C 3. + C - 3. 23 B

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Q: (2g(x)-3, xsI x>1" "rx)dx = 18, then g(x)dx = Let f(x) - %3D A) 5. B) 6. C) 7. D) 8. E) 9. A) B) c)…

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Q: Find the value of df-1/dx at x = f(a). 15) f(x) = x3 - 12x2 - 4, x 2 8, a = 2 1 1 B) - C)- 36 D) 44…

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Q: x+ 18 (d) J3 dx x2+x-6

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Q: Solve the D.E. 3(3x2 + y?) dx - 2xy dy = 0 A x = c(x2 + 3y²) B x = c(9x² + y²) c) x = c(x² + 9y²) D…

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Q: d4y + dx2 d²y ) Obtain a particular solution for + + y = x³ + 2x + 1 dx4 dx

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Q: dy If = 3x² – 1 and if y= -1 when X=1 then y= dx (A x³ +1 B -x3 +x-1 © x3 – x+1 D x3 - x-1

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Q: 5. Find a solution f(x) to the equation (D³ – D² + D – 1)f(x) = 0 such that f(0) = 1, f'(0) = 0,…

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Q: 2- 2-3 + 2y = e* d²y dx2 e 3x dx

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Q: 2x3- x² + x + 2 dx = D dx find A+B+ C+D. + x+1 + Consider x4 + x3 4 O 3 O 2 O 5

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Q: f(x) dx - f g(x)dx - f¹ g(x)dx A. -1 B. 7 C. 1 D. -7

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Q: S²- 16-x2 A 2 B) 8 0 None 4 E dx is equal to

A: I am attaching image so that you understand each and every step. Option "C" is correct answer.

Q: f(x) dx = 4 and 0 1₂ 2 +S²g(x)dx? 3 f(x) dx + -2 10 2 g(x) dx = 6, what is

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Q: Q4. f(x)=5 and 1(x)de=8 dx = 5 and f(x) dx = 8 then f(x)dx a) -3 b) -13 c) 13 d) 3 dx is given by

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Q: d’y The general solution of dx 3 dx2 + = 0 is 0 is dx O y = (C¡ + C2x + C3x²) %3| O None of these O…

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Q: a) | f(x)dx = -10 %3D 4 b) f(x) dx = -10.5 4 c) f(x) dx = -17.5 10 d) / f(x) dx = 9 %3D 10 e) -5…

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Q: dF h(x) = x² + 5x – 1, g(-8) = 3, g'(-8) = –9, and F(x) = g(x)h(x). Find %3D dx

A: We know, ddx[u(x)v(x)]=v(x)ddx[u(x)]+u(x)ddx[v(x)]

Q: Given f(x)dx =0 and f²f(x)dx = 끝. 11 A 6 55 B 6 11 C 5 D evaluate S" 3f(x)dx - [2f(x)dx.

A: Here, given that: ∫-11f(x) dx=0, ∫01f(x) dx=116

Q: + 2x3 d?y dx2 dy Q5. Solve x* dx3 + xy = 1 - dx

A: According to the given information it is required to solve the differential equation:

Q: 4 2 + e )dx y2 x =

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Q: y = f(x) X2 f(x) = (m - 1)x2 - 4x + m-2 X, = ? %3D A) 1 B) 2 C) 3 D) 4 E) 5 f(x) = mx2 - 4x - 3m %3D…

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Q: Find the value of df-1/dx at x= f(a). f(x) = x² - 4x + 2; a = 5 1 O A. 6 1 O B. 14 1 OC. 10 O D. 6

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Q: x2  d2y/dx2 - 3xdy/dx + 3y=0  what is the general solution

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Q: Q2) Solve the D.E dy – (2x/1– y²)dx = 0

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Q: S(3x².fu)+x°, f'(x) dx =24 so, so, f(2) = ) %3D

A: We have to solve the given question. Derivative of the function f(x) can be written as f'(x) Product…

Q: 2x²+x+1 A (x - 1)(x + 1)(x-2) dx = ₁+ A -2 (B) None 3 D E 15 B x+1 + x-2 d. dx, then the value of C…

A: Given  ∫2x2+x+1x-1x+1x-2dx = ∫Ax-1+Bx+1+Cx-2 dx

Q: Given the equation of y = g(x) satifies dy + (1 – 2x)y = 4x, x > 0, g(1) = 3(e² – 1). dx Solve an…

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Q: 4 B + x+3 dx = (x- 1) (x² – 9) dx, what is A- B+C? If X-3 A) 0 B) 1 D

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Q: dy b. If y = V(B1e* – B2 x³ + B3 x + B4 + In(x))5 , then find the dx A1=1 A2=5 B1=4 B2=6 B3=2 B4=1

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