1 / | | _________ | / 2 | \/ 16 - x dx | / 0
TrigSubstitutionRule(theta=_theta, func=4*sin(_theta), rewritten=16*cos(_theta)**2, substep=ConstantTimesRule(constant=16, other=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), context=16*cos(_theta)**2, symbol=_theta), restriction=And(x < 4, x > -4), context=sqrt(-x**2 + 16), symbol=x)
Добавляем постоянную интегрирования:
Ответ:
1 / | | _________ ____ | / 2 \/ 15 | \/ 16 - x dx = ------ + 8*asin(1/4) | 2 / 0
3.95793371424034