3- , thei a) E{f,(y\x)} =- exp(- o/27(2-r²) 20ʻ(2-r²)' 1 b) E{f, (x)f;(y)}=- 2.noV4-r

Q: · (x−1)² √x d) f - dx =

A: To evaluate the following integral.

Q: Calculate y" and y'''. y = 4t 3 - 9t 2 + 7

A: Given that  y = 4t3 - 9t2 + 7 We have to calculate y'' and y'''. First we find y'. y' = ddty     =…

Q: \text { 5. } \frac{d}{d x}[c]=0

A: To show: That ddxc=0. Concept used: Power rule of differentiation: xn'=n·xn-1 Calculation: The…

Q: (f) / sec“ y dy. tan5

A:

Q: dx (4-2²)° (뿌): O none of these 1/2 11/8

A:

Q: 12. Suppose we want to know whether or not the mean weight of a certain species of dog is equal to…

A:

Q: e2 6. - dx -Find 1

A:

Q: ©Use TMe Phopentos to Eselaate dx=D4 (2) 3 x da= 2

A:

Q: x2+1 - dx x4-x²+1

A:

Q: 2 1. xe*dx

A: The value of the integral can be evaluated as following ∫02xexdx

Q: xe* хе dx. J (x + 1)2

A:

Q: -sech? (In 3.x)

A: We can find the answer as below.

Q: |(5z* + 3z*) (4x³ + 3x*)° dæ

A:

Q: Find (2a° + 3x*) dæ + C

A: We evaluate given integral

Q: Evaluate: 3 A 1–x*) 2 + C 3 (1-x*) ² + C --(1-x*) ² +C D 1-x*) 2 + C 3

A:

Q: fostp Ex=(Xzy)=-3:52-25)

A:

Q: 0o dx Q1. (a)Find /," 3

A:

Q: Q2-Prove that

A:

Q: (cosh ar +h)dr

A:

Q: JA 1 dx. /4-

A: ∫14-x2dxFormula∫11-x2dx=sin-1(x)+C

Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

Q: A = - 1)³² dx - (x - 1)³dx + 5²0x

A:

Q: dy =Log. Loc

A: Using logarithmic property we can solve this problem.

Q: Evaluate y' at the point (2,2) 5x3y - 2x2 = 72

A: The given equation is 5x3y-2x2=72. Rewrite the above equation as follows:…

Q: (хе* + 4e* + 4eУ + 4lny) dx + ( хеУ + — dy %3D0;B у (0) — 0

A:

Q: xy2 = 8 at (2,2)

A: Substitute x=2 and y=2 in the given function xy2

Q: Evaluate les-). d 3x dx OA (3x³- x?)e3x²-x?-1 O A. ² – x² – 1 OB. O B, e oc (9x² - 2x)e³x³-x? OC.…

A: