## anonymous one year ago Y=1+srwt(x), y=1+.5x. Find the area of region

1. anonymous

First equation is =1+sqrt(x)

2. IrishBoy123

$$y=1+\sqrt{x}$$ $$y=1+\frac{1}{2}x$$

3. anonymous

So what is the area?

4. Australopithecus

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)

5. Australopithecus

So can you find your intercepts?

6. anonymous

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

7. IrishBoy123

so the area is $$\large \int_{0}^{4} (1 + \sqrt{x}) - (1+\frac{1}{2}x) \ dx$$ $$\large = [ \ (x + \frac{2}{3}x^{3/2} - x - \frac{1}{4}x^2) \ ]_{0}^{4}$$ $$\large = [ \ ( \frac{2}{3}x^{3/2} - \frac{1}{4}x^2) \ ]_{0}^{4}$$ $$\large = \frac{2}{3}(4)^{3/2} - \frac{1}{4}(4)^2 = \frac{4}{3}$$

8. IrishBoy123

did you get that also?

9. anonymous

Yes

10. IrishBoy123

cool! good night!