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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    First equation is =1+sqrt(x)

  2. IrishBoy123
    • one year ago
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    \(y=1+\sqrt{x}\) \(y=1+\frac{1}{2}x\)

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  3. anonymous
    • one year ago
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    So what is the area?

  4. Australopithecus
    • one year ago
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    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
    • one year ago
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    So can you find your intercepts?

  6. anonymous
    • one year ago
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    No and I'm late for dinner can u just share the area?

  7. IrishBoy123
    • one year ago
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    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
    • one year ago
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    did you get that also?

  9. anonymous
    • one year ago
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    Yes

  10. IrishBoy123
    • one year ago
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    cool! good night!

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