Unformatted text preview: [15 pts] A man is driving his car on a perfectly ﬂat surface. The location of the car at time t, for t Z 1? is given by the coordinates
t t 1
I(t)=f\/u+1du, y(t)=/1‘.I'1+Edn.
1 1 Find the distance traveled by the man in his car between times t = 1 and t = 2. (a) (12 points) Use the Fundamental Theorem of Calculus and properties of deﬁnite integrals to
show that if f is continuous on [11, b] and if 3(3) and 11(3) are diﬂerentiable functions whose values lie in [(1, b]1 then
”(3} U u
— ( mm) = smug—I — (mug—I. (h) (8 points] Find (with justiﬁcation] the value of :1: that maximises the value of the integral 3+3
1 as — t] dt. ...
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 '07
 BERMAN
 Calculus

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