Integrate the following using substitution 1) z5 (9z6 – 7)8 dz 2) S dy 4 y3 2-5y4

Q: dy dx 23 X + 24 2メ+ツ

A:

Q: 3(y-2) 1- 3y

A:

Q: Find Df, Rf : Y= 3/(2x+1)

A:

Q: (2x)(x-y+5)(5y)

A: Firstly, we multiply 2x by each term of x-y+5

Q: 5. Use the substitution method to evaluate r1 5xe32+2 dr. 0.

A: To determine the value of the integral.

Q: ッーメー 5 X-39) メ1に

A:

Q: /1-y² S(y² + x²) dzdxdy -10

A:

Q: (x - 3 bxy + 2 b?y?) (xdx + ydy) = xdy-ydx %3D

A:

Q: D2 – 5D +6)y=3xex+2x2 , y(0)=0,y,(0)=1

A: Given differential equation is homogeneous ordinary differential equation. To solve this equation…

Q: (3y-2 Jdy y+2y+17

A: Topic:- integration

Q: メ Find dy S-3xメ+)X-2) (x211) (2X+3)

A: We have to find the derivative of y

Q: dz 22 z²+4z S

A:

Q: J(2m-a)(√m² - am - a² dm

A: The given integral ∫2m-am2-am-a2dm. We have to find the integral value.

Q: 3) S dz z3-z2-6z

A: In the question it is asked to calculate the integral of the following function given:

Q: y = 2t + t2 – 2(In t)² d.

A: y = 2t + t2 - 2(lnt)2

Q: (x²9) Lim X→3 (X+3)

A: To calculate

Q: 2 d) ²₂t(t4 +3t)dt -2

A: We need to solve ∫-22t(t4+3t)dt

Q: 3. (D5 –Dª – 2D³ +18D² –31D+15)y =0

A: Given differential equation is D5-D4-2D3+18D2-31D+15y = 0

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

A:

Q: 3y +5 (5y-7)2 dy

A: We can find the integration as below.

Q: Find the product. (2² + y) (3x² – y)

A: We need to find the product of the given expression,                 x2+y3x2-y

Q: 1. Expand the brackets a. X(x+2) b. X2(x+x2) c. 3x(x-y) d. 4x2(2-3x) e. X3(1+2x -x2) f.…

A: We can solve this by properties of power of polynomials xm*xn = xm+n

Q: seA (D²-D-6)y(x) = xe sled a 1 1 *(5x + 2) - y,(x) = xe"(5x- 2) - y,x)= xe" (5x +2) -i 50 50 50

A:

Q: (x² D² - xD + 3) y = x²(Inx)4

A:

Q: y(4)-8y" + 16y=0

A: To solve the differential equation

Q: (2z–1)dz S 2z2 –6z+5

A: