(Solved): Use the definite integral and the Fundamental Theorem of Calculus to solve the following problem. ...

Use the definite integral and the Fundamental Theorem of Calculus to solve the following problem. A particle moves along a line in such a way that its velocity at time \( t \) is \( v(t)=t^{2}-4 t-32 \) (measured in meters per second). (a) The displacement of the particle during the time period \( 1 \leq t \leq 11 \) is \( \quad \) meters. (b) The distance traveled by particle during the time period \( 1 \leq t \leq 11 \) is \( \quad \) meters. Hint: