1 / | | ________ | / 2 | \/ 1 - y dy | / 0
Integral(sqrt(1 - y^2), (y, 0, 1))
TrigSubstitutionRule(theta=_theta, func=sin(_theta), rewritten=cos(_theta)**2, substep=RewriteRule(rewritten=cos(2*_theta)/2 + 1/2, substep=AddRule(substeps=[ConstantTimesRule(constant=1/2, other=cos(2*_theta), substep=URule(u_var=_u, u_func=2*_theta, constant=1/2, substep=ConstantTimesRule(constant=1/2, other=cos(_u), substep=TrigRule(func='cos', arg=_u, context=cos(_u), symbol=_u), context=cos(_u), symbol=_u), context=cos(2*_theta), symbol=_theta), context=cos(2*_theta)/2, symbol=_theta), ConstantRule(constant=1/2, context=1/2, symbol=_theta)], context=cos(2*_theta)/2 + 1/2, symbol=_theta), context=cos(_theta)**2, symbol=_theta), restriction=(y > -1) & (y < 1), context=sqrt(1 - y**2), symbol=y)
Add the constant of integration:
The answer is:
/ | | ________ // ________ \ | / 2 || / 2 | | \/ 1 - y dy = C + |-1, y < 1)| / \\ 2 2 /
Use the examples entering the upper and lower limits of integration.