Section 4.5 homework
Calculus I
Andy Long

#7, p. 336

(* #7, p. 335, from 4.5: *)
Integrate[x*Sin[x^2],x]

#16, p. 336

(* #16, p. 335 *)
Integrate[Sin[Sqrt[x]]/Sqrt[x], x]

#20, p. 336

(* #20, p. 335 *)
Integrate[Sqrt[x]Sin[1+x^(3/2)], x]

#25, p. 336

(* #25, p. 335 *)
Integrate[Sqrt[Cot[x]]Csc[x]^2, x]

#38, p. 336

(* #38, p. 336 *)
Integrate[x Cos[x^2], {x,0,Sqrt[Pi]}]

#39, p. 336

(* #25, p. 335 *)
Integrate[Sec[t/4]^2, {t,0,Pi}]

#43, p. 335

(* #43, p. 335 *)
Integrate[(1+2x)^(-2/3), {x,0,13}]

#25, p. 339

(* #25, p. 339 *)
Integrate[Sin[2x]/Cos[2x]^2, {x,0,Pi/8}]

#43, p. 339

(* #43, p. 339 *)
b=3;
a=0;
n=6
dx=(b-a)/n
f[x_]:=Sin[x^3];
data=Table[f[a+dx/2+dx*(i-1)],{i,6}]
N[dx*Total[data]]