Question

Y=1+srwt(x), y=1+.5x. Find the area of region

Answer 1

First equation is =1+sqrt(x)

Answer 2

\(y=1+\sqrt{x}\)
\(y=1+\frac{1}{2}x\)

Answer 3

So what is the area?

Answer 4

Steps:

1.

Find where both curves intercept using systems of equation

2.

Figure out which function is larger by simply inputing a number inbetween the two intercept bounds

3.

Integrate in respect to x using intercepts as bounds for the intgrals

Set up an integral for the larger function
Set up an integral for the smaller function

5.

Subtract the larger function integral from the smaller function integral

If you get a negative you subtracted them incorrectly ( you confused the smaller function for the larger function)

Answer 5

So can you find your intercepts?

Answer 6

No and I'm late for dinner can u just share the area?

Answer 7

so the area is \(\large \int_{0}^{4} (1 + \sqrt{x}) - (1+\frac{1}{2}x) \ dx\)

\(\large = [ \ (x + \frac{2}{3}x^{3/2} - x - \frac{1}{4}x^2) \ ]_{0}^{4}\)

\(\large = [ \ ( \frac{2}{3}x^{3/2} - \frac{1}{4}x^2) \ ]_{0}^{4}\)

\(\large = \frac{2}{3}(4)^{3/2} - \frac{1}{4}(4)^2 = \frac{4}{3}\)

Answer 8

did you get that also?

Answer 9

Yes

Answer 10

cool!

good night!