Question

Evaluate

∫ √tanx. sec4x dx

π

4

Also integrate the definite integral using MATLAB command.

Answer 1

$I=\int^{\pi /4}_0 \sqrt{tanx}sec^4x dx=\int^{\pi /4}_0 \sqrt{tanx}(1+tan^2x)sec^2xdx$

$tanx=t,sec^2x=dt$

$I=\int(t^{1/2}+t^{5/2})dt=2t^{3/2}/3+2t^{7/2}/7=2tan^{3/2}x/3+2tan^{7/2}x/7|^{\pi/4}_0=$

$=2/3+2/7=20/21$

MATLAB code

syms x
expr=sqrt(tanx)*(secx)^4;
F=int(expr,0,pi/4)