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A bus drives along a straight road. At time t seconds its speed is v(t) = 3t² + 2 metres per second…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A bus drives along a straight road. At time $t$ seconds its speed is $v(t) = 3t^2 + 2$ metres per second. The distance covered between two times is the area under the speed graph. Find the distance covered from $t = 0\ \text{s}$ to $t = 3\ \text{s}$ , and the distance covered from $t = 1\ \text{s}$ to $t = 3\ \text{s}$ .

Need a reminder? The key ideaShow

If $F' = f$ and $f$ is continuous on $[a, b]$ , then the signed area is $F(b) - F(a)$ . Where $f$ changes sign, split the interval and add the sizes to get the area.

\displaystyle \int_a^b f(x)\,dx = \left[F(x)\right]_a^b = F(b) - F(a).

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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A bus drives along a straight road. At time t seconds its speed is v(t) = 3t² + 2 metres per second…

The worked solution

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