Assignment:
Note: x is used as a letter only not as a multiply sign
Q1. Find the volume of the solid generated by revolving the region enclosed by y= x^(1/2), y=0, x=4 about the line x=6.
Q2. Find the arc length of the graph of the function y = x^(3/2) - 1 over the interval [0,4]
Q3. Integrate
∫ [(Pi / 2) / 0] x cos x dx
Q4. Integrate
∫ (cos^3) x (sin^2) x dx
Q5. Integrate
∫ ((1) / ((x^2) (25-x^2)^(1/2))) dx
Q6. Integrate
∫ (((3x^2)-7x-2) / ((x^3)-x)) dx
Q7. Integrate
∫ ((x-1) / ((x^3)+(x^2))) dx
Q8. Find the limit of the improper integral
∫ [∞/1] (x+2) e^(-x) dx if it exists
Q9. Find the arc length of the curve given in parametric form by
x= t^2, y= 2t, 0 ≤ t ≤ 2.
Provide complete and step by step solution for the question and show calculations and use formulas.