A ball is projected from a point O with an initial
velocity u and angle θ with the horizontal ground.
Given that it travels such that it just clears two walls
of height h and distances 2h and 4h from O respectively.
(a) find the tangent of the angle θ
(b) The time of flight of the ball
(c) The range of the ball.
Evaluate ∫_0 ^1 (x^2 /(√(1+x^3 )))dx and given that I_(n ) =∫_0 ^1 x^n (1+x^3 )^(−(1/2)) dx
show that (2n−1)I_n =2(√2)−2(n−1) for n≥3.
Hence evaluate I_8 , I_7 and I_6