Question on finding g(t)?

Let g’’(t) = sint + cost, g(0) = 2 and g’(π) = -1. Find g(t).

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  • ben e
    Lv 7
    1 decade ago
    Favorite Answer

    g’’(t) = sin t + cos t

    So g'(t) = -cos t + sin t + C

    Since g’(π) = -cos(π) + sin(π) + C = 1 + C = -1, C = -2 and

    g'(t) = -cos t + sin t - 2.

    g(t) = -sin t - cos t - 2t + C

    g(0) = -sin(0) - cos(0) - 2*0 + C = -1 + C = 2, so C = 3

    g(t) = -sin t - cos t - 2t + 3

  • 1 decade ago

    g''(t) = sint + cost

    integrating both sides

    g'(t) = -cost + sint + c

    since g'(pi) = -1

    g'(pi) = -cos(pi) + sin(pi) + c = -1

    -(-1) +0 + c = -1

    c + 1 = -1

    c = -2

    so g'(t) = -cost + sint - 2

    again integrating

    g(t) = -sint - cost - 2t + c1

    since g(0) = 2

    g(0) = -sin(0) - cos(0) - 0 + c1 = 2

    0 - 1 + c1 = 2

    c1 = 3

    so g(t) = -sint - cost - 2t + 3

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