Question

(a) Evaluate∫[

x

√x

2+1

]dx.

(b) Use MATLAB to generate some typical integral curves of f(x) =

x

√x

2+1

over the

interval (−5,5).

Answer 1

a)

$\int\frac{x}{\sqrt{x^2+1}}dx=\int\frac{d(x^2)}{2\sqrt{x^2+1}}dx=\sqrt{x^2+1}+c$

b)

syms x
f=sqrt(x^2+1);
int(f, x, -5, 5)