5 questions are in attached files

Problem 6
Velocity of Rocket = v km/s
And velocity as a function of time is given as,
v(t) = 6e2t + t
Now from the relation of velocity and displacement,
v = ????
????

ds = v dt
ds = (6e2t + t)dt
O integrating both sides we get,
s = 3e2t + t2/2 + C
since as per the question it is given that at t= 0
s = 10 hence
C = 10
So finally the expression of displacement will be,
s = 3e2t + t2/2 + 10 (Answer)
Problem 7
(a) Equation of circle with center at origin is given by
X2 + Y2 = a2 , where a is radius
In this question radius is 2 so writing the above equation in terms of x we get
Y = √4 − ??2
Hence on interating from 0 to 2 we get
∫ ?????? 20 = ∫ √4 − ??
2???? 20 =...