Интеграл sqrt(100-x^2) (dx)

1. TrigSubstitutionRule(theta=_theta, func=10*sin(_theta), rewritten=100*cos(_theta)**2, substep=ConstantTimesRule(constant=100, 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=100*cos(_theta)**2, symbol=_theta), restriction=And(x < 10, x > -10), context=sqrt(-x**2 + 100), symbol=x)$$

2. Добавляем постоянную интегрирования:

   $$
   begin{cases} frac{x}{2} sqrt{- x^{2} + 100} + 50 {asin}{left (frac{x}{10} right )} & text{for}: x > -10 wedge x < 10 end{cases}+ mathrm{constant}

Ответ:

begin{cases} frac{x}{2} sqrt{- x^{2} + 100} + 50 {asin}{left (frac{x}{10} right )} & text{for}: x > -10 wedge x < 10 end{cases}+ mathrm{constant}

1
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| __________ ____
| / 2 3*/ 11
| / 100 – x dx = 50*asin(1/10) + ——–
| 2
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0

9.98330824361109

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| __________ // __________
| / 2 || / 2 |
| / 100 – x dx = C + |< /x x*/ 100 - x | | ||50*asin|--| + --------------- for And(x > -10, x < 10)| / 10/ 2 /