dy d.x B) Does not exist If y = e- ln x then A) 0 when x = = 1 is O 210 18 D) 1/12 E) e

Q: 6t et Y=n-x, then find fcy)

A: Here X~Bin(n,p) ; where X=0,1,2,.......,n

Q: A5. The value of the definite integral dx is b) - 8 c) 24 d) 1.5

A: We have to find the value of the given definite integral.

Q: 5) Solve the Non-linear second ODE: d²y + 3 x² y dx? y? = x² ) (dy %3D

A: Given: Non-linear second order differential equation is 3 x2 y d2ydx2+y2=x2(dydx)2

Q: dy Q3) Find dx for 3(x? + y?) ² = 100xy

A: Here, the derivative dydx is obtained by implicit differentiation. Thus to find the derivative first…

Q: {G) = -2x+5 firid f(2)

A: To find: The value of f1. Given: The function is fx=-2x+54. Calculation: Substitute x=1 in…

Q: 2dx J x (3(ln x)2 + 12 ln a – 15) -

A: Answer

Q: Calculate a) ∫x ln x dx. b) ∫cos (2x) dx c) ∫ 2x +1 dx        x² - 1 d) ∫20   (x − 1) 25dx

A:

Q: /3 In 3 7e*dx 1+ e 2x

A: Given: ∫0ln337ex1+e2xdx To find: We have to find the value.

Q: Sketch and evaluate the reverse in tegral 9/x dy dz

A: Consider the provided integral,

Q: 2tan-(x) dx = (b- in4 (+ In2 (- in4 (e)None In2

A:

Q: d Prove that (x") = n x"-1 dx

A:

Q: e tan (e") dx Vsec2 (eª) – 7

A: Use substitutions method for finding the integral.

Q: d y then is dx? x=1-8t Suppose y = 5t* +2

A:

Q: TT Evaluate A eit dt 4 0.

A: This problem can be solved easily by the substitution method.

Q: Prove that Jn (x) X good dx=1. n

A:

Q: 6 S dx x+3 n = 10 ) 2 A

A:

Q: 3. S (?-) 32x In|x| dx + C 3 2 In 3

A:

Q: 3 a) Given fg(x)dx=5, [[3g(x)– 4h(x)]dx = 27 . i) Find [h(x)dx . ii) Hence, evaluate [4x – 3h(x)]dx.

A:

Q: y = ), Bind X+3 Q4l y= (Sinx) (x²p1) (x +3)3 4 find 5.

A:

Q: d) Bessel function, Show that So Jo(x) dx = 1.

A:

Q: Solve: dy dr = y +e*y?

A: The given differential equation is dydx=y+exy2. Rewrite the differential equation as,…

Q: 9. 3y'e" dx dy

A: To solve the integral

Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

A: Given- y2=x2+sinxy-π24 To Find- The value of dydx at π2,1 and considering that value as β and then…

Q: dx Select one: O True O False

A: Given statement is

Q: 22 2. Solve the following, te' dt. 0-2 a) 7.8036 b) 11.807 c) 14.034 d) 19.611

A:

Q: 5x sinx dx = %3D

A:

Q: 10) Solve for x when 2 log x - log 100 = 2 a) 105 b) 10° c) 10' 10⁰

A:

Q: 19. Evaluate fln(x)dx A) ln(x) + x + C B) x ln(x) − x + C C) e* -x + C ex D) In²(x) + C 2 E) None of…

A:

Q: Given dr/dt=Cx²- 8x) / (6142) and dyldt = - 12 xy, Salve for: %3D A) xCt) B) yet

A: Given dxdt=x2-8x642 Rewriting the differential equation: dxdt=x2-8x17dxdt=7x2-8xdxx2-8x=7dt

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A: Since you have asked multiple questions in single request.so we will be answering only first…

Q: Prove that : L₁₁ (1-x²) PP dx = 0. 2n(n+1) 2n + 1 . mn. m1 = 11. m, ne N

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Q: S f(x)dx

A:

Q: d b) [ 4e*(In x) ] dx

A:

Q: (d) DNE (e) 2. Calculate each of the following i: (a)/ sec2 (x) dx (b) 3 (d) In(x) dr (e) 0. 1. dx…

A:

Q: Use the reduction formula: [(In 2)" dx = 2(In x)" — n f (In 2)¹-1, times. First application of the…

A: Given: ∫(ln x)n dx=x(ln x)n-n ∫(ln x)n-1 dx     ........(1) By using the above result we have to…

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A:

Q: 8. o Vx² + 9 (A) -2 (B) 15 (C) 1 (D) 2 (E) 5

A:

Q: Since S xf'(x)dx = 2x3 + 2x2 + c if f(0) = 1, f(1) how much is it worth? O A) 7 O B) 15 OC) 8 O D) 5…

A: