calculate ∫6,3 9x²dx, given the following. ∫2,3 x dx = 2.5 ∫2,3 x²dx = 19/3 ∫3,6 x²dx = 63 ∫6,3 9x²dx = □…
calculate ∫6,3 9x²dx, given the following. ∫2,3 x dx = 2.5 ∫2,3 x²dx = 19/3 ∫3,6 x²dx = 63 ∫6,3 9x²dx = □ (type an integer or a simplified fraction.)
Answer
Explanation:
Step1: Use integral property $\int_{a}^{b}cf(x)dx = c\int_{a}^{b}f(x)dx$
$ \int_{6}^{3}9x^{2}dx=9\int_{6}^{3}x^{2}dx$
Step2: Use integral property $\int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx$
$9\int_{6}^{3}x^{2}dx=- 9\int_{3}^{6}x^{2}dx$
Step3: Use integral property $\int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx$ for $\int_{3}^{6}x^{2}dx$, so $\int_{3}^{6}x^{2}dx = 63$
$-9\times63=- 567$
Answer:
$-567$