22.2  integral_0^20 sqrt(400-20t) dt

22.3  Plot[Piecewise[{{2000t-1000t^2, 0.1>t>0.0}, {190, 0.3>t>0.1}, {190-900(t-0.3), 0.4>t>0.30}}], {t, 0, 0.4}]
      integral 2000t-1000t^2 dt from 0 to 0.1 + integral 190 dt from 0.1 to 0.3 + integral 190-900t dt from 0 to 0.1

22.4  plot[{t^3-6t^2+8t},{t,0,6}]
      integral |t^3-6t^2+8t| dt from 0 to 6 
      integral t^3-6t^2+8t dt from 0 to 6 

22.5  Plot[Piecewise[{{5t, 4>t>0}, {20, 10>t>4}}], {t, 0, 10}]
      s=integral_0^4 a*t dt
      a=56*a/(integral_0^4 a*t dt + integral_4^10 4a dt)

22.6  a) 1950-integral_0^4 9.8*t dt
      b) 2130-integral_0^13 9.8*t dt
      c) 1950-integral_0^4 9.8*t dt - integral_4^(45+13) 5 dt > 2130-integral_0^13 9.8*t dt 

22.8  integral t/(t^2+1) dt from 0 to 5

22.9 (integral 9.8 dx from 0 to 1.5) - 4

22.10 integral 80/3-250t dt from 0 to 8/75

22.18 0.624 * integral (50-t) dt from 0 to 50

22.19 (680*9.81 * integral 1 dt from 0 to 7) + 18 * 9.81 integral t dt from 0 to 7

22.21 8048.6 * integral 3^2*pi*(9-x) dx from 0 to 9

22.22 11475.6 * integral pi*x*(4-x) dx from 0 to 4