WRITE COMMANDS TO SOLVE FOLLOWING USING MATLAB
I. Evaluate the following (Reduction equations)
clear
syms x
f = sin(x)^45
f = 
int(f,0,pi/2)
ans = 
II. Gamma Function:
gamma(1/2)
ans = 1.7725
gamma(9/4)
ans = 1.1330
gamma(-1/2)
ans = -3.5449
gamma(3/4)
ans = 1.2254
gamma(-5/2)
ans = -0.9453
syms x
int(x^4*exp(-4),0,inf)
ans = 
syms x
f = x^2*exp(-2*x^2)
f = 
int(f,0,inf)
ans = 
eval(ans)
ans = 0.1567
f = exp(-sqrt(x))*x^3
f = 
int(f,0,1)
ans = 
eval(ans)
ans = 0.1033
III. Beta Function :
beta(5,4)
ans = 0.0036
beta(1/2,3/2)
ans = 1.5708
beta(1,1/2)
ans = 2.0000
Represent following beta functions in the form of gamma functions
clear
syms x y
expand(beta(x,y))
ans = 
expand(beta(x^2,y^3))
ans = 
IV. Error Function: (Correct to three decimal places accuracy )
Note: vpa function is used to display answer till 3 decimal places
vpa(erf(0.3),3)
ans = 
vpa(erf(0.5),3)
ans = 
vpa(erf(0.8),3)
ans = 
V. Differentiation Under Integral Sign (Using Symbolic and Numeric math toolbox)