Question

matlab

mpyutico y Piol yinj 3) (6 pts) Find a) int b) trapz c) integral (2x2 + 2x - 1) dx using the following functions 4) [6 ptsThe value of

Answer 1

Code: In the code below in trapz we have taken x value at space of 1 from -3 to 1

clc
clear

syms x
f = 2*x^2 + 2*x - 1;
I_int = int(f, -3, 1)

x = -3:1;
y = @(x)2.*x.^2 + 2.*x - 1;
I_trapz = trapz(x, y(x))

I_integral = integral(y, -3, 1)

Output:

I_int =

20/3

I_trapz =

8

I_integral =

6.6667

Code: But if we take smaller step size in x for trapz it gives better accuracy

clc
clear

syms x
f = 2*x^2 + 2*x - 1;
I_int = int(f, -3, 1)

x = -3:0.01:1; %just taken a smaller step size
y = @(x)2.*x.^2 + 2.*x - 1;
I_trapz = trapz(x, y(x))

I_integral = integral(y, -3, 1)

Output:

I_int =

20/3

I_trapz =

6.6668

I_integral =

6.6667