Give an example, with justification, of a periodic function which is not even.
Sine function is odd. sin(-x) = - sin
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Find the volume of the solid obtained by revolving the curve
X = a cos3 θ , y = a sin 3 θ about the y-axis.
Trace the curve x(y2 + 4) = 8, stating all the points used for doing so.
Evaluate 
Find the area enclosed by the curve r = a (1 - cos θ).
- If x sin y = sin (p + y), p ∈ R, show that sin p dy/dx + sin 2 y = 0.
A jogger runs from her home to a point A, which is 6 km away. For there 6 km, she begins by running at a constant speed till she reaches a hilly portion 2 km from her home. Here her speed slows down while she runs up the hill, which is a 1-km run. Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance from her home. Also find the range of this function.
Differentiate tan -1 [sin x - cos x /sin x + cos x]
with respect to 1/2 x.