How large should n be to guarantee that the Trapezoidal Rule approximation to 8 4 +22x³ - 144x² − 3x + 5) dx is accurate to within 0.1. n = 72 X How large should n be to guarantee that the Simpsons Rule approximation to √₁² (-2² +22x³ (-x¹ +22x³ - 144x² − 3x + 5) dx is accurate to within 0.1. n = 8 X Hint: Remember your answers should be a whole numbers, and Simpson's Rule requires even values for n

Q: Evaluate: a) +7sec2 x dx /x 1+x?

A:

Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

A:

Q: 8. dx :) x² +9 0.

A:

Q: 3.) Integrate using an appropriate technique: 24100 dx (show all steps) 4x2 + 24x+100

A: We have to evaluate

Q: Prove : (x2 + 2x + 2 )dx > 0

A: The given integral is ∫-10x2+2x+2-x2dx The integral has been rewritten∫-10x2+2x+12x2dx Apply…

Q: .Find the left endpoint sum and the right endpoint sum for |(x² +3)dx 3 using four equal width…

A: We have ∫35(x2+3)dx∆x=5-34=12Left end point sum=∑i=15mi∆xi…

Q: 2) Sxsec²(4x² – 5) dx. 3) S3x Vī– 2x² dx .

A:

Q: Evaluate. 9- xp- dx%3D Evaluate. dx | dx = Evaluate. dx dx =

A: As per guideline we have to solve 1st 3 parts

Q: 2 3 Find 3/7 ) da 6x2 | _ -

A: We need to evaluate the following integral ∫6x2-2x+3x5-3xdx

Q: Finds 2) S 12x-31 dx

A:

Q: 5. Use the substitution method to evaluate So 3x²+2 x3 + 2x +37 dx.

A: Topic = Integration

Q: Find the length of MO in square LMNO if MO=2x+4 and LN=8x-8,

A:

Q: 6) Evaluate 0.8 1 0 dx 4x² +4

A:

Q: 2. f(e³x + √x +9)dx 3x

A:

Q: 3 7) Evaluate: f(-x² + 4x − 1)dx 1

A: Given, ∫13(-x2+4x-1)dx

Q: Compute the following. [4x16 +8x5 – 13x +18x17/9+7x-8+3] dx

A:

Q: Evaluate the integral: · √2 9 1 + x² -dx

A:

Q: What is the discriminant of the PDE? 2 d2u/dx2= 8 d2u/dt2

A:

Q: PERPARA EPIFFERITEURE HIFCERERE dx SURASEULEET EXPLOREZPIER MERASAKASH FLERENCE r 7)Evaluate ↑n(x²)…

A: I have stated the used formulas in the solution.