2 4 E (x² + 2)V4 – x² dx 3

Q: x2+x-2 dx If S dx can be resolved into A f+B S f(x)dx + D § g(x)dx , then (x2–1)(2x-x²) Lif(x)dx –…

A:

Q: +2メ+2 2=f(x.y)-4xy 3. +2メ+2y2= T %3=

A: Derivative: - The function's derivative is the equation we discovered. The derivative is defined as…

Q: С 20 3x-1 хр. -X (3+3 (2) j² dx a Лх lo XS хр sự X Сў-12.d:

A:

Q: 3. YA x=y² – 2 ソ=1 x= e' y=-1

A: Solution Question 3  Given,  The curves  x = y2 -2    and   x = ey We have to find the area of…

Q: (a) y=e**' In(x² +2) 2+w? (b) f(w)=ln. w -2

A:

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

A: Linear differential equation

Q: n: (5y*x - 2y7)dy-(a-3x²y5)dx = 0

A:

Q: 3. (10 – 6y +e 3) dx -3x 2dy = 0 -

A: According to our guideline, we can solve only first question of multiple question. If you want…

Q: 5. (1+2xVx2 - y² )dx-(2yVx2-y? )dy =0

A:

Q: n: y" – 9y = 0; e3x; e-3x

A:

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: 1-3х 4. y2x – 32 dx V2x – 3x²

A:

Q: e そo 3/2 S-スス)ん dx (4x²+1)-

A: We have to find the value of the integral  ∫(1-x2)3/2x6dx Note- since you have posted multiple…

Q: 8. 4 13 what is 3 | f(v)dv? Given that f(x)dx 4 8

A: Given: ∫48fxdx=133

Q: +4x 6) y' = Ans.: y-x =e +C. 3y - 2xye"

A: According to the guidelines in case of multiple questions we are only allowed to do first question,…

Q: 8. (x² + 2xy 4y²) dx - (x² - 8xy - 4y²) dy = 0. ANS. x² + 4y² = c(x +

A: A homogeneous differential equation is given by, x2+2xy-4y2dx-x2-8xy-4y2dy = 0. The objective is to…

Q: X f(x) =< Q 14/15 7 x + 1 3 ;0≤x≤2 ;2≤ x ≤3 5 Tov Then what is the result of 3 (fx) dx 1

A:

Q: x+2 a) f- =dx V2x-x² |xIn(x+1)dx b)

A: Given that  (a) ∫(x+2)/√(2x-x2) dx   (b) ∫x ln(x+1)dx Here we have to calculate the given integral.

Q: (xi+axy-3)dk + 2x°dy -0 3)ck +2x²dy =0 Qxt -3x*y? +x = 3 +2xy -3n =0 O Option 3 O Option 1 x+ 6x…

A:

Q: 16. Using integration by parts to solve 2√4x²+k A. -√4-x² + k √4x²+k -2√4x²+k B. C. x³ dx √4-x² and…

A: Given: ∫x3dx4-x2

Q: Calculate the derivative.

A:

Q: 23. What is dx? 3 – e4r e2z + V3 In e2r + V3 In |e2x а. +C C. +C 2 e2x – V3 V3 /3. b. V3 +C V3 +C 2x…

A:

Q: solution of the di dy x + 4y = * x2

A:

Q: 3 2 ²²(4-x²) dy dx = 7 0 true O False

A:

Q: 2) (Зx2у + 4eУ)dx + (x3 + 4хеУ + 2у)dy

A:

Q: dx 4. S хV25-х2 5+Vx2-25 + C а. 5+Vx2-25 b. In + C c. --In 5+v25-x2 + C с. 5 d. None of the above

A:

Q: e-(2²+x³) dy dæ x=-0 Jy=0

A:

Q: 6-9 d x.dy 2.

A: A double integral is given. We need to evaluate the double integral.

Q: 9) y = e4x² + x A) dy dx 8xe2x + 1 B) dy - 8xex2 dx %3D + 1 C) dy dy - 8xe4x2 dx — 8хе + 1 %D D) + 1

A: We have to find

Q: x-e -2r -dx x²+e-2« *2(x-e-2«) A x²+e-2r xp- – 2(x-e-2x) dx x2+e-2r B -2x 2+e =21 dx x²+e-2¢…

A:

Q: d³y 6. dx3 23- 33+ 10y = 0 dx2 dx

A:

Q: dv 9. S- V3v-2a 10. S(5 – 3y)*dy

A:

Q: 1 4. xarctan(x)dx IT -2 а. IT -2 b. 4 с. 4 d. T-2 е. 2

A: We have to find integration by using integration by Parts.

Q: 2 (2x² + y²) dx - xydy = 0 X2 O = C y² +4x²2 ○ In x + In (²4²) = C Oy - 1 = x - 3+ C .2 X O = C…

A:

Q: 1. y" + 4y' + 4y = e-2x %3D x2

A: We find the complementary solution Yc and Particular integral Yp The complete solution is sum of Yc…

Q: •7 49–x² r83–x²-y² x dz dy dx %D 0, -15+x²+y²

A: I am attaching image so that you understand each and every step.

Q: 1-S dx ; 1-e-2x y2 + 2r +

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

Q: x + 5 dx = (9 – x²) + C 5 x 5 V9 - + C 9 V9 - x2 *e 5 x 9 + C 9 - x2 + C 4 9 - 18 v9 - 5 x 18 v9 -…

A: Given:              ∫x+59-x232 dx

Q: 1 вхось xа(1 — x)bdx - = 6xº1 Bx®1 - x)dx /0

A:

Q: A. Using the basic formulas, integrate the following: 1. fx(x² +2)²dx 2. S(2V – 3x)²dx 3. fx³Vxdx 4.…

A: Note: As per our guidelines we are supposed to answer only 3 sub parts under one question. kindly…

Q: 2 f(x) dx = 2, f(x) dx = 3, and g(x) da = 4. 1. | (2f(x) + g(x)] da = 2.

A: If ∫01fxdx=2, ∫12fxdx=3 and ∫02gxdx=4Find, ∫022fx+gxdx

Q: 10. f (Se e-3x XE -3e*-4e*)dx 4e)dx e-2

A: Solution: The expression can be written as

Q: .3 2х+x-1 4. J dx х3+x2—4х-4

A:

Q: 1- 2 - x = e»/2 x3 dy 2- (2xe + e*)dx + (x² + 1)e'dy = 0

A: Disclaimer:Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 1 e*(6x-15x +9x') =x'e* D² -D+3 true Error

A: e-2x(6x-15x2+9x3) =(D2-D+3) x3e-2xRight Hand Side:(D2-D+3) x3e-2x =(D2x3e-2x) - D (x3e-2x) + 3x3e-2x…

Q: 2(3у-7) Зу-7 3y – 7dy + С 2. ans. Jx(1-x²)°dx - (1-х^2)6 + C 8 3. ans.

A:

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

A:

Q: 1 - dx = x² – 6x+8 -4 +C х-2 (A) In x- 2 In 2 (B) +C - 4 (C) 극미(x-2)(x-4)|+ (D) n|(x-4)(x+2)|+c (E)…

A:

Q: Find the derivatives of the given functions. (Part D and E)

A: d)  We will need the quotient rule. For that assume u and v and find u' and v'

Q: (b) Evaluate |(2x+3)V x² + 3x – 5 dx , by using substitution method.

A: