The shaded area on the graph above is equal to:

Question

BlackTom AI · Accepted Answer

The provided data for this question is incomplete.

What was given:
- The question text states: 'The shaded area on the graph above is equal to:'
- The displayed polynomial on the graph appears to be y = x(x + 2)(x − 3).
- The answer field shows 'a. 21 1/12 sq. units', but the answer options list is empty.

Because there are no answer choices to evaluate, I cannot identify which option is correct or provide a choice-by-choice analysis as requested.

What would typically be needed to determine the shaded area:
- A clear statement of the interval over which the shaded area is computed (e.g., between two x-intercepts or over a specified x-range).
- Confirmation whether the shaded region is the area between the curve and the x-axis, i.e., the integral of |f(x)| over the interval, or a signed area if the problem defines it differently.
- If the shaded region corresponds to the region where the curve is below the x-axis (as appears to be the case between x = 0 and x = 3 for f(x) = x(x + 2)(x − 3)), compute the area as the integral of −f(x) over that interval.

If we assume the shaded region is the area between the curve y = x(x + 2)(x − 3) and the x-axis from x = 0 to x = 3 (where f(x) ≤ 0), the calculation would be:
- f(x) = x(x + 2)(x − 3) = x^3 − x^2 − 6x.
- Area = ∫ from 0 to 3 of −f(x) dx = ∫ from 0 to 3 (−x^3 + x^2 + 6x) dx.
- This evaluates to [−x^4/4 + x^3/3 + 3x^2] from 0 to 3 = (−81/4) + (27/3) + 3·9 = (−81/4) + 9 + 27 = (−81/4) + 36 = (144/4 − 81/4) = 63/4 = 15.75 square units.

Thus, with the common interpretation of the shaded region being the area between the curve and the x-axis from x = 0 to x = 3, the area would be 63/4 square units (15.75), which does not match the provided option '21 1/12'. However, since the options are missing, this is only a computed result under one plausible interpretation.

In summary, the key blocking issue is that the answer options are not provided. If you can share the complete list of answer choices, I can walk through each option in detail and explain which is correct and why, using the appropriate integral setup for the shaded region.

MUF0092 Mathematics Unit 2-SEM 1-2025 8.1 Integration Reminder

The shaded area on the graph above is equal to:

查看解析

登录即可查看完整答案

类似问题

Find the signed area produced by:[math: A=∫364cos(5x)dx](square units)Calculate your answer correct to 4 decimal places.(Note: Make sure your calculator is in radian mode.)

Find the area produced by:[math: A=∫16(8x3+12x2+4)dx](square units)

Evaluate the integral.

Evaluate the integral.

Graph the integrand and use geometry to evaluate the integral.

Find the area of the shaded region.

Graph the integrand and use geometry to evaluate the integral.

Solve the problem. Suppose that = 3. Find and .

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单