Question

Math

Posted 6 months ago

```
The curves $x=7 y+18$ and $x=2 y^{2}+19 y+18$ are graphed.
Which expression represents the area bounded by the curves?
Choose 1 answer:
(A) $\int_{-6}^{0}\left(-2 y^{2}-12 y\right) d y$
(B) $\int_{-6}^{0}\left(2 y^{2}+26 y+36\right) d y$
(c) $\int_{-4.75}^{18}\left(-2 y^{2}-12 y\right) d y$
() $\int_{-4.75}^{18}\left(2 y^{2}+26 y+36\right) d y$
```

Sign in to unlock the answer

Answer from Sia

Posted 6 months ago

Solution by Steps

step 2

Setting $7y + 18 = 2y^2 + 19y + 18$, we get $2y^2 + 12y = 0$

step 3

Solving $2y^2 + 12y = 0$ gives $y(y + 6) = 0$, so $y = 0$ or $y = -6$

step 4

The area between the curves from $y = -6$ to $y = 0$ is given by the integral $\int_{-6}^{0} \left[(7y + 18) - (2y^2 + 19y + 18)\right] dy$

step 5

Simplifying the integrand, we get $\int_{-6}^{0} \left(-2y^2 - 12y\right) dy$

step 6

Therefore, the correct expression for the area is $\int_{-6}^{0} \left(-2y^2 - 12y\right) dy$

A

Key Concept

Area between curves

Explanation

To find the area between two curves, you need to integrate the difference of the functions over the interval determined by their points of intersection.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Unlock Smarter Learning with AskSia Super!

Join Super, our all-in-one AI solution that can greatly improve your learning efficiency.

30% higher accuracy than GPT-4o

Entire learning journey support

The most student-friendly features

Study Other Question