Assignment:
Q1. R is the region that lies between the curve y = (1 /( x2 + 4x + 5) ) and the x-axis from x = -3 to x = -1. Find:
(a) the area of R,
(b) the volume of the solid generated by revolving R around the y-axis.
(c) the volume of the solid generated by revolving R round the x-axis.
Q2. Evaluate: ∫ sinh6 x cosh xdx.
Q3. Given f(x) = csch-1 (1 / x2), find f'(x).
Q4. Evaluate ∫ ( (log3 x) / 2x) dx.
Provide complete and step by step solution for the question and show calculations and use formulas.