X -1 1 E(X), E(Y), D(X), D(Y), Cov(X,Y), PXF- Y-1 1 0.35 0.45 0 0.20

Q: dx (x2 - 169) 3/2 *> 13

A: Use the trigonometric substitution and simplify the integration than solve it.

Q: 1 Laplace transforms Calculate the Laplace transforms of (i) H₂(t) cosh (3t), where cosh (at) = 1/²…

A: Solution: (i) let, f(t) = H2(t)cosh(3t)                   = H2(t)[(1/2)(e3t + e-3t)]…

Q: (e + x + 2)dx 3.

A: The sum rule for integration states that ∫fx+gxdx=∫fxdx+∫gxdx. The integration formula for…

Q: S. 2 x 2 x +9 -dx

A:

Q: 4 12d2= -dx = x² - 1 (A) B D 4 ln x² - 1| + C 2 ln+C 4sin ¹x + C 4tan ¹x + C

A:

Q: x3-27 dx 2. ズ-3

A:

Q: e* -1 dx 2x Find,

A: ∫ex-1e2xdx

Q: ㅇ 1/x dx 39 -1 +3

A:

Q: f cos4x dx

A: According to guidelines, we must answer only one of the multiple questions given.So I answered only…

Q: E(X)=5 and E(Y)=8 What is E(X+4Y)?

A: From the properties of expectation:-EaX+bY=aEX+bEY

Q: (x+2) dx (x + 3)*(x +1)³

A: ∫-20x+2(x+1)3(x+3)3dxSubstitute u=(x+1)(x+3)→dudx=2x+4→dx=12x+4du=12∫1u3du

Q: For f(x) = x? – 5x - 6, find f(2), f'(2), and f(3) – f(2). f(2) = a. b. f'(2) %3D c. f(3) – f(2) -

A: The given function is fx=x2-5x-6

Q: x² - x + 12 dx x3 + 2x

A:

Q: x + 7 dx J (x²)(x + 2)

A:

Q: 5x * Example (4): Evaluate dx (х - 1)(х — 2)(х + 3) |

A:

Q: x²-3x - 7 √(x² + x + 2) (2x - 1) dx

A:

Q: -1 df Find for f(x) = x+3 dx 2x+5 at X= 3 . 1 A 25 (в -25 1 81 81

A: topic - derivative of a Inverse function

Q: 2x + 3 If f(x) = then x – 2 dy / (x – 2)² dx ||

A: fx=2x+3x-2

Q: d 1 (csc"' x) = dx sc""x) = - .2 -1

A: Solution:- here we have to prove that  ddx(csc-1x)=-1xx2-1

Q: 3 dx Jo 4x² + 5x + 1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 2x+5 - dx- (x² – 1)(x+2)

A:

Q: f(x) = e−x,    n = 5

A: Given:          fx=e-x ,n=5 A Maclaurin series is given by fx=∑n=0∞fnan!xn Here fx≈Px=∑n=05fnan!xn…

Q: (x - 1)ex (x + 1)³ -dx

A:

Q: 2x + 3 If f(x) then x + 2 dy /(x+ 2)2 %3D dx

A: Given: f(x)=2x+3x+2 The objective is to find the numerator a of the derivative of the given…

Q: Find the values of a and b such that a = b + [¹ f(x) dx − [*f(x) dx = f*f(x) dx. - 11

A: Given,

Q: (4(x2-1) dx x²(x+2)

A: We will use partial fraction here

Q: Let f (x) = x - 1 and g (x) = x² (x + 1). Evaluate Se 3 + dx f(x) g(x) You must show all steps.

A: Integration of e-3x+f(x)/g(x)Where f(x)=x-1,  g(x)=x2(x+1)

Q: X (2x + lny)dx + = dy = 0 Y y(1) = 1

A:

Q: 2х + 10 dx Evaluate 2(x – 4)

A: topic - indefinite integration