## Trending News

Promoted

# Question on finding g(t)?

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

### 2 Answers

Relevance

- ben eLv 71 decade agoFavorite 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

- mohanrao dLv 71 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

Still have questions? Get your answers by asking now.