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Math Help - Help me with my calc final take home!

  1. #1
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    Help me with my calc final take home!

    Antiderive:
    a) 3-x/1+9x^2 (split the fraction it says)

    b) sin(-2x)/[1-cos(2x)]^5

    c) -2/sqroot(9-x^2)

    d) cox(x)/1+sin^2(x)



    2. Consider that graph of y=-x^2+4x-3 and the area that lies under the curve in quad 1.
    a)estimate the area using sumseq with 5 rectangles and using left endpoints

    b)calculate exact area (is this fnInt function ?)


    c)calc. average value of the function in the first quadrant.




    3. Determine all relative max,min, inflection points (correct to 2 decimals)
    for y=.2x^3-x^2-x^2-.8x+4. exhibit a labeled graph







    Thanks for the help guys, this is part of my study guide for the final, i will finish it tomorrow and check my answer with the site to see what i did wrong. Thanks in advance!
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  2. #2
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    d) cos(x)/1+sin^2(x)
    let u = sin(x)
    du = cos(x)

    int cos(x)/(1+u^2) {du/cos(x)}
    cancel the cosine
    int 1/(1+u^2) du

    it becomes inverse tan integrate
    tan^-1(u) + C
    tan^-1(sin(x)) + C
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  3. #3
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    c) -2/sqroot(9-x^2)
    pull away the constant
    -2 int 1/(sqt{9 - x^2} du
    and by the inverse sine rule which is
    sin^-1(u/a)

    integrate
    -2sin^-1(x/3) + C
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  4. #4
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    b) sin(-2x)/[1-cos(2x)]^5
    from trig identity
    int (-2sin(x)cos(x)) / (1-(1-2sin^2(x)))^5 dx
    -2 int (sin(x)cos(x)) / (2sin^2(x))^5 dx
    cancel the sins
    -2 int (cos(x)) / (32sin^9(x))
    -2/32 int (cos(x)) / (u^9) {du / cos(x)} <<< derivative of sin
    -1/16 int 1 / u^9 du

    -1/16 [u^(-9+1)/(-8)]
    substitute
    1/128 * sin^-8(x)
    1/128 * csc^8(x) + C
    or
    csc^8(x)/128 + C
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  5. #5
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    a) (3-x)/(1+9x^2) (split the fraction it says)
    int (3/1+9x^2) - int(x / (1+9x^2))
    for integral 1 let u = 3x, du = 3dx
    int (3/(1+u^2)) {du/3}
    int (1/(1+(3x)^2)
    tan^-1(3x)

    for integral 2 let u = (1+9x^2), du = 18xdx
    int (x/(1+(u)) {du /18x}
    cancel tha x
    1/18 int (1/(1+9x^2))
    1/18 ln(1+9x^2)

    tan^-1(3x) - 1/18 ln(1+9x^2) + C
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  6. #6
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    awesome, can someone show me how to do B and C of question 2. and i have question 3 done
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  7. #7
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    #2b
    Your exact area is the integral:
    Attached Files Attached Files
    • File Type: doc A.doc (34.5 KB, 26 views)
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