Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To evaluate the integral [tex]\(\int_1^3 6 f(x) \, dx\)[/tex], we can use the property of integrals that allows us to factor out a constant. This property states that for any constant [tex]\(c\)[/tex],
[tex]\[ \int_a^b c \cdot f(x) \, dx = c \cdot \int_a^b f(x) \, dx. \][/tex]
Given the integral [tex]\(\int_1^3 f(x) \, dx = 5\)[/tex], we will apply this property with [tex]\(c = 6\)[/tex]:
[tex]\[ \int_1^3 6 f(x) \, dx = 6 \cdot \int_1^3 f(x) \, dx. \][/tex]
Substituting the given value of [tex]\(\int_1^3 f(x) \, dx\)[/tex]:
[tex]\[ \int_1^3 6 f(x) \, dx = 6 \cdot 5. \][/tex]
Thus,
[tex]\[ \int_1^3 6 f(x) \, dx = 30. \][/tex]
Therefore, the answer is [tex]\(30\)[/tex].
[tex]\[ \int_a^b c \cdot f(x) \, dx = c \cdot \int_a^b f(x) \, dx. \][/tex]
Given the integral [tex]\(\int_1^3 f(x) \, dx = 5\)[/tex], we will apply this property with [tex]\(c = 6\)[/tex]:
[tex]\[ \int_1^3 6 f(x) \, dx = 6 \cdot \int_1^3 f(x) \, dx. \][/tex]
Substituting the given value of [tex]\(\int_1^3 f(x) \, dx\)[/tex]:
[tex]\[ \int_1^3 6 f(x) \, dx = 6 \cdot 5. \][/tex]
Thus,
[tex]\[ \int_1^3 6 f(x) \, dx = 30. \][/tex]
Therefore, the answer is [tex]\(30\)[/tex].
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.