Untitled

> #solutions to Quiz 4
restart;

> R2:=(12.5)^2-(12.5-h)^2;
r2:=(3.5)^2-(3.5-h)^2;

R2 := 156.25-(12.5-h)^2

r2 := 12.25-(3.5-h)^2

> Pi*int(R2-r2,h=0..x);

9.*Pi*x^2

> diff(log(cos(x)^2+1),x);

-2*cos(x)*sin(x)/(cos(x)^2+1)

> int(x/exp(x^2),x=0..1);

-1/2*exp(-1)+1/2

> f:=1/3*sqrt(x)*(3-x);

f := 1/3*x^(1/2)*(3-x)

> df:=diff(f,x);

df := 1/6*(3-x)/x^(1/2)-1/3*x^(1/2)

> int(2*Pi*f*sqrt(1+df^2),x=0..3);

3*Pi

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