y sinx2 1Solutionysinx21 y1sinx2 arcsiny1x2 sqrtarcsiny1x

Solution

y=sin(x^2)+1
y-1=sin(x^2)

arcsin(y-1)=x^2

sqrt(arcsin(y-1))=x

now we will try to find at what point it crosses 0 of y axis

x=sqrt(arcsin(-1))= sqrt(3pi/2 )

V=Integral( pi * x^2) bound 0 to sqrt(3pi/2)

=Integral(pi* arcsin(y-1) dy

integral of arcsin is sqrt(1-y^2)+x*arcsin(y)

substitute the bound get the answer