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Math Help - Two quick Questions...

  1. #1
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    Two quick Questions...

    1.



    The base of a certain solid is the area bounded above by the graph of y =f(x) =25 and below by the graph of y= g(x)= 16x^2. Cross-sections perpendicular to the x axis are squares.

    Use the formula <br />
V = \int_a^b A(x)dx<br />

    Thus the volume of the solid is V= ?


    2.

    To find the length of the curve defined by

    y = 2x^2 +3x

    from the point (0,0) to the point (1,5), you'd have to compute

     \int_a^b f(x)dx<br />

    where a = ?
    where b = ?

    and f(x)= ?

    Please Help I am so stuck.

    Thanks As always

    qbkr21
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  2. #2
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    Hello, qbkr21!

    Here's help with #2 . . .


    2) To find the length of the curve defined by: . y \:= \:2x^2 +3x .from (0,0) to (1,5)

    you'd have to compute: . \int_a^b f(x)\ dx . . . where a = ? . where b = ? . and f(x)= ?
    You're expected to know the Arc Length formula: . L \;=\;\int^b_a\sqrt{1 + \left(\frac{dy}{dx}\right)^2}\,dx

    Since \frac{dy}{dx} \:=\:4x + 3, then: . 1 + \left(\frac{dy}{dx}\right)^2\:=\:1 + (4x + 3)^2 \;=\;16x^2 + 24x + 10

    . . Therefore: . L \;=\;\int^5_1\sqrt{16x^2 + 24x + 10}\,dx


    Can you answer the questions now?

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