Solve the following problems on bond papers (maximum 3 bond papers) with ½ inch margin on all sides. Show your complete solution. Solutions should be handwritten. 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

Q: x + 5 dx 0. 6.

A: Question from definite integration.

Q: Stan5 x sec³ x dx

A:

Q: 1. S- VE dx 6 Vĩ

A: Indefinite Integration

Q: 1 dx х x³Vx²

A: We have to integrate  ∫22 1x3x2-1 dx.

Q: 1. L= V1 + 16x6 dx

A: First, we factor out 16 from the radical term, So, it becomes,

Q: 5. Change of variable 2 x dx 3x+1 a.

A: Given function, ∫12x3x+1dx

Q: Solve X(Inx - Iny)dy - ydx = 0 %3D

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: (2x³-9x²+2) dx from x = 6 to x = 11

A: Given: ∫2x3-9x2+2dx   from x=6 to x=11

Q: Find √√3 x² +3 x² +1 dx

A:

Q: If a= 1/x + 1/y, what is the value of 1/a?

A:

Q: Sx sech2 x² dx

A: Given:  Integral of xsech2x2

Q: 1. L,(3x? – 2x³)dx 2. (x? – 1)va dx

A: We will solve the problem.

Q: Find y". y = x(3x + 1)* y" =L

A: Given function is  y= x(3x+1)4  We have to find : y".

Q: 1. [(2x-3) (4x2– 12x)* dx

A:

Q: 1.y =z+1

A:

Q: 2. ſ xºcos(4x)dx

A: ∫x0 cos4xdx

Q: 2. dx ***S 1 - x4

A: Integral

Q: 2. S xV5x-x2 dx

A:

Q: 27. x(2 + x') dx Jo

A: integration

Q: 1. Solve for 'x': vx + v2x +7 = 8

A:

Q: Solve the following In(x) Ⓒdx ((*√x) In (²))

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: 4. S sec(inx) dx x

A: ∫seclnxxdx