Integrate[Sin[x]^2,x]

Manipulate[n+4,{n,0,5}]

Sum[x^2,{n,0,10}]

Sum[x^n,{x,0,10}]

Sum[x^3,{x,0,k}]

Integrate[Sin[s],s]

D[Sin[x]^3*Exp[x],x]

f[x_]:=Exp[-x^2/2]/Sqrt[2Pi]

Plot[f[x],{x,-3,3}]

(Subscript[\[Placeholder], \[Placeholder]])

Integrate[f[x],{x,-1,1}]

N[Erf[(1/(Sqrt[2]))]]

Integrate[f[x],{x,0,Infinity}]

f[2]

N[(1/((E^2) (Sqrt[2 π])))]

g[x_]:=If[x>-1/2 && x<1/2,1,0]

Plot[g[x],{x,-2,2}]

(Subscript[\[Placeholder], \[Placeholder]])

g2[x2_]:=Integrate[g[y]*g[x2-y],{y,-Infinity,Infinity}]

Plot[{g[y2],g2[y2]},{y2,-3,3}]

\[Placeholder]

(Subscript[(Subscript[(Subscript[(Subscript[\[Placeholder], \[Placeholder]]), \[Placeholder]]), \[Placeholder]]), \[Placeholder]])(Subscript[\[Placeholder], \[Placeholder]])

g2[y2]

g[y2]

g4[y4_]:=Integrate[g2[x4]*g2[

(y4-x4)],{x4,-Infinity,Infinity}]

g4[y

g4[y4_]:=Integrate[g2[x5]*g2[y4-x5],{x5,-Infinity,Infinity}]

(Subscript[(Subscript[\[Placeholder], \[Placeholder]]), \[Placeholder]])Plot[g4[y5],{y5,-4,4}]

1+1

Plot[{g[x6],g2[x6],g4[x6]},{x6,-4,4}]

LinguisticAssistant

(Subscript[\[Placeholder], \[Placeholder]])

g4[aa]

g4[.3]

Plot[Sin[x],{x,-4,4}]

Plot3D[Sin[x]*Cos[y],{x,-4,4},{y,-4,4}]

nn=NormalDistribution[0,1]

PDF[nn,3]

N[(1/((E^(9/2)) (Sqrt[2 π])))]

Plot[CDF[nn,xa],{xa,-3,3}]

CDF[nn,2]

N[(1/2) Erfc[-(Sqrt[2])]]

Mean[nn]

VarianceEstimatorFunctione0

Variance[nn]

n3=MultinormalDistribution[{0,0},{{1,.5},{.5,1}}]

Plot3D[PDF[n3,{za,zb}],{za,-2,2},{zb,-2,2}]

PDF[n3,{zc,zd}]

Integrate[%,{zd,-Infinity,Infinity}]

D[Sqrt[x],x]

CDF[nn,2]

N[(1/2) Erfc[-(Sqrt[2])]]