anonymous
  • anonymous
Y=1+srwt(x), y=1+.5x. Find the area of region
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
First equation is =1+sqrt(x)
IrishBoy123
  • IrishBoy123
\(y=1+\sqrt{x}\) \(y=1+\frac{1}{2}x\)
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anonymous
  • anonymous
So what is the area?

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Australopithecus
  • 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)
Australopithecus
  • Australopithecus
So can you find your intercepts?
anonymous
  • anonymous
No and I'm late for dinner can u just share the area?
IrishBoy123
  • IrishBoy123
so the area is \(\large \int_{0}^{4} (1 + \sqrt{x}) - (1+\frac{1}{2}x) \ dx\) \(\large = [ \ (x + \frac{2}{3}x^{3/2} - x - \frac{1}{4}x^2) \ ]_{0}^{4}\) \(\large = [ \ ( \frac{2}{3}x^{3/2} - \frac{1}{4}x^2) \ ]_{0}^{4}\) \(\large = \frac{2}{3}(4)^{3/2} - \frac{1}{4}(4)^2 = \frac{4}{3}\)
IrishBoy123
  • IrishBoy123
did you get that also?
anonymous
  • anonymous
Yes
IrishBoy123
  • IrishBoy123
cool! good night!

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