Answer to Question #199580 in Calculus for VPM

Question

3. The distance travelled by a train on a straight track in the first two seconds is given by

𝑠= ∫²₀ 20(1−𝑒^−𝑡)𝑑𝑡20

Find the distance travelled in Metres

Answer 1

$\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx$

$=20\cdot \int _0^{-2}-1+e^udu$

$\int _a^bf\left(x\right)dx=-\int _b^af\left(x\right)dx,\:a<b$

$=20\left(-\int _{-2}^0-1+e^udu\right)$

$=20\left(-\left(-\int _{-2}^01du+\int _{-2}^0e^udu\right)\right)$

$=20\left(-\left(-2+1-\frac{1}{e^2}\right)\right)$

$=-20\left(-\frac{1}{e^2}-1\right)$

$22.70670$m