This is not your father’s area?

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Presentation transcript:

This is not your father’s area? Integration This is not your father’s area? http://nm.mathforcollege.com

They are thinking of replacing all three of them with Pow The economy is so bad that the following is happening with Snap, Crackle and Pop They are thinking of replacing all three of them with Pow Kelloggs hired a “cereal” killer to kill them all Snap is spreading rumors that “Pop was a rolling stone” They are selling smack, crack and pot, respectively. http://nm.mathforcollege.com

Ask me what I should already know The pre-requisite questions http://nm.mathforcollege.com

The exact mean value of the function f(x) from a to b is http://nm.mathforcollege.com

Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of y x a 5 7 2 b c -7 -2 12 Cannot be determined http://nm.mathforcollege.com

Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of y x a 5 7 2 b c -7 -2 7 12 http://nm.mathforcollege.com

Physical examples http://nm.mathforcollege.com

Distance Covered By Rocket http://nm.mathforcollege.com

Concentration of Benzene u= velocity of ground water flow in the x -direction (m/s) D = dispersion coefficient (m2) C0= initial concentration (kg/m3) http://nm.mathforcollege.com

Is Wal*** “short shifting” you? Roll Number of sheets 1 253 2 250 3 251 4 252 5 6 7 8 254 9 10 http://nm.mathforcollege.com

Calculating diameter contraction for trunnion-hub problem http://nm.mathforcollege.com

END http://nm.mathforcollege.com

7.02 Trapezoidal Rule http://nm.mathforcollege.com

This artist’s name is Young Scooter Kendrick Lamar Bodaga Bamz 2 ChainZ http://nm.mathforcollege.com

Two-segment trapezoidal rule of integration is exact for integration of polynomials of order of at most 1 2 3 4 http://nm.mathforcollege.com

In trapezoidal rule, the number of segments needed to get the exact value for a general definite integral 1 2 1 googol infinite http://nm.mathforcollege.com

In trapezoidal rule, the number of points at which function is evaluated for 8 segments is 9 16 17 http://nm.mathforcollege.com

In trapezoidal rule, the number of function evaluations for 8 segments is 9 16 17 http://nm.mathforcollege.com

The distance covered by a rocket from t=8 to t=34 seconds is calculated using multiple segment trapezoidal rule by integrating a velocity function. Below is given the estimated distance for different number of segments, n. n 1 2 3 4 5 Value 16520 15421 15212 15138 15104 The number of significant digits at least correct in the answer for n=5 is 1 2 3 4 http://nm.mathforcollege.com

The velocity vs time is given below The velocity vs time is given below. A good estimate of the distance in meters covered by the body between t=0.5 and 1.2 seconds is t(s) 0.5 1.2 1.5 1.8 v(m/s) 213 256 275 300 213*0.7 256*0.7 256*1.2-213*0.5 ½*(213+256)*0.7 http://nm.mathforcollege.com

7.05 Gauss Quadrature Rule http://nm.mathforcollege.com

The morning after learning Gauss Quadrature Rule… http://nm.mathforcollege.com

Autar Kaw is looking for a stage name. Please vote your choice. The last mindbender Қ (formerly known as Kaw) Kid Cuddi Kaw & Saki http://nm.mathforcollege.com

is exactly http://nm.mathforcollege.com

A scientist would derive one-point Gauss Quadrature Rule based on getting exact results of integration for function f(x)=a0+a1x. The one-point rule approximation for the integral is http://nm.mathforcollege.com

For integrating any first order polynomial, the one-point Gauss quadrature rule will give the same results as 1-segment trapezoidal rule 2-segment trapezoidal rule 3-segment trapezoidal rule All of the above http://nm.mathforcollege.com

A scientist can derive a one-point quadrature rule for integrating definite integrals based on getting exact results of integration for the following function a0+a1x+a2x2 a1x+a2x2 a1x a2x2 http://nm.mathforcollege.com

For integrating any third order polynomial, the two-point Gauss quadrature rule will give the same results as 1-segment trapezoidal rule 2-segment trapezoidal rule 3-segment trapezoidal rule None of the above http://nm.mathforcollege.com

The highest order of polynomial for which the n-point Gauss-quadrature rule would give an exact integral is n n+1 2n-1 2n http://nm.mathforcollege.com

END http://nm.mathforcollege.com

Physically, integrating means finding the Area under the curve from a to b Area to the left of point a Area to the right of point b Area above the curve from a to b http://nm.mathforcollege.com

The velocity of a body is given as v(t)=t2. Given that the location of the body at t=6 is 27 54 63 Cannot be determined http://nm.mathforcollege.com

The velocity of a body is given as v(t)=t2. Given that the distance covered by the body between t=3 and t=6 is 27 54 63 Cannot be determined http://nm.mathforcollege.com