Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Use the concept of the definite integral to find the total area between the graph off(x) and thex-axis, by taking the limit of the associated right Riemann sum. Write the exact answer. Do not round. (Hint: Extra care isneeded on those intervals wheref(x) < 0. Remember that the definite integral represents a signed area.)f(x) = 3x + 3 on [0, 2]

Use The Concept Of The Definite Integral To Find The Total Area Between The Graph Offx And Thexaxis By Taking The Limit Of The Associated Right Riemann Sum Writ class=

Sagot :

ANSWER

15 square unit.

EXPLANATION

Step 1:

Recall that the right endpoint Riemann sum for

[tex]\begin{gathered} ^{}\int ^b_af(x)dx\text{ is given by } \\ \frac{b-a}{n}\sum ^n_{k\mathop=1}f(a+\frac{b-a}{n}k) \end{gathered}[/tex]

Step 2:

Note, if f(x) is continuous, then:

[tex]\lim _{n\to\infty}\frac{b-a}{n}\sum ^n_{k\mathop{=}1}f(a+\frac{b-a}{n}k)\text{ = }^{}\int ^b_af(x)dx\text{ }[/tex]

Step 3:

Now, applying the limit of the Reimann sums to evaluate the integral:

[tex]^{}\int ^2_0(3x+3)dx\text{ }[/tex]

Please, carefully check my working:

Hence, using the concept of the definite integral, the total area between the graph of f(x) and the x-axis by taking the limit of the associated right Riemann sum is 15 square unit.

View image LuciannaN708362
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.