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Math Help - Find the area enclosed by the given curves

  1. #1
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    Find the area enclosed by the given curves

    I need help in solving this..... Please and Thank You
    And explain throughly for me please because i am 100% confused....
    Find the area of the region in the first quadrant bounded by the line , the line , the curve , and the x-axis.
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  2. #2
    MHF Contributor red_dog's Avatar
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    Solving the system formed by the two curves we find x=\frac{1}{4}

    Then the area is

    A=\int_0^{\frac{1}{4}}8xdx+\int_{\frac{1}{4}}^1\fr  ac{1}{\sqrt{x}}dx

    Can you continue?
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  3. #3
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    no i can't.... i don't even know what you did.... lol
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  4. #4
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    Quote Originally Posted by red_dog View Post
    Solving the system formed by the two curves we find x=\frac{1}{4}

    Then the area is

    A=\int_0^{\frac{1}{4}}8xdx+\int_{\frac{1}{4}}^1\fr  ac{1}{\sqrt{x}}dx

    Can you continue?
    Quote Originally Posted by dizizviet View Post
    no i can't.... i don't even know what you did.... lol
    The first thing you should do is draw the graph of the lines y = 8x and x = 1 and the curve y = \frac{1}{\sqrt{x}} and then shade the required region. Have you done that?

    You need to find where the line and the curve intersect. Solve 8x = \frac{1}{\sqrt{x}} to get the x-coordinate.

    The required region consists of two seperate parts. The part between the line and the x-axis, and the part between the curve and the x-axis. Find the area of each part.

    There are several pre-calculus skills you need to have competency in. It might be wise to go back and revise those skills (finding where curves intersect, solving equations, drawing graphs etc.)
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  5. #5
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    ok thanks alot you helped alot if i need help again i'll be sure to ask +)
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