Вопрос
Select all expressions matching the value of indefinite integral int x^2(1-2x+x^2)dx (x^3(6x^2-15x+10))/(30)+C (x^3)/(3)(-x^2+(x^3)/(3))+C -(x^4)/(2)+(x^5)/(5)+C
Решения
4.5
(166 Голоса)
Лидия
Экспертная проверка
профессионал · Репетитор 6 лет
Ответ
To determine which expressions match the value of the indefinite integral
, we need to evaluate the integral.First, let's simplify the integrand:
Now, we can integrate term by term:
Integrating each term separately:
Putting it all together:
Now, let's compare this result with the given options:1.
: Simplifying this expression:
This expression does not match the result we obtained.2.
: Simplifying this expression:
This expression does not match the result we obtained.3.
: This expression matches the result we obtained.Therefore, the correct answer is: