Original formula = integer (0 to 2pi) and integer (0 to1) er2 * rdr = 2pi *1/2er2 | (1,0) = PI (E- 1).

2、y''=cosx+x

y'=sinx+ 1/2*x^2+c 1

y'(x=0)=c 1=0

y=-cosx+ 1/6*x^3+c2

y(x=0)=- 1+c2=- 1

Found c2=0

So y =-cosx+ 1/6 * x 3.

3、V=V 1-V2

V 1 is the volume from 0 to 1 after y = x 2 is rotated.

V2 is the volume of y=x from 0 to 1 after rotation.

V 1 =π* ZDZ = 1/2 *π is under integer sign.

V2 is a cone.

V2= 1/3pi

V= 1/6pi