Integration v(t)=t^2-t-2 Find Displacement and Distance in the first 3 seconds IB SL Math

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CORRECTION: Solution 1: 2/7 x^(7/2)+C
Q1. ∫▒〖x^2 √x〗 dx,x≥0
Q2. Given √y=4∜x-2x^(-1/4),x≥0. Find ∫▒y dx,x≥0.
Q3. Given ∫▒(5a/x^3 -2ab) dx=24x-15/x^2 +C. Find value of a and b.
Q4. A particle moving in a straight line and has a velocity v(t) m/s and displacement is s(t) m at time t seconds where ,0≤t≤10. The particle’s acceleration is given by a(t)=2 m/s^2. The particle has initial conditions of v(0)=-7 and s(0)=10 m. By finding expressions for v(t) and s(t), determine when the particle is moving away from the origin.
Q5. The cross section of a drainpipe is defined by f(x)=〖0.02x〗^4-0.4x^2-2.5,
-5≤x≤5
Find the maximum depth of the pipe.
Find the cross-section area of the pipe.
Q6. Given graph of f(x)=x^2-6x+5 and g(x)=x-1.