Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Suppose [tex]\int_1^3 f(x) \, dx=5[/tex], [tex]\int_3^8 f(x) \, dx=-4[/tex], and [tex]\int_3^8 g(x) \, dx=6[/tex]. Evaluate the integrals in parts a-d.

a. [tex]\int_1^3 6 f(x) \, dx = \square[/tex] (Simplify your answer.)

Sagot :

GinnyAnswer
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].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.