Could anyone please help us out with these problems even just to show how to begin. It would be great and I would be very grateful. I have an exam coming up and I need to get these problems sorted.
Show that the volume of the solid obtained by rotating the part of circle of x^2 + y^2 = 1 that lies between x =0 and x = 1/2 about the x axis is (11pi)/24 cubic units.
Find the antiderivative between e and 1 of (4 ln(x) + 5) / x dx using substitution of w = 4ln(x) + 5
A searchlight rotates at a rate of 3 revolutions per min. Its beam of light hits a wall that is 10km away and produces a dot of light that moves horizontally along the wall. At what speed is the dot moving when the angle between the beam of light and the line through the searchlight perpendicular to the wall is pi/6
Find the slope of the curve x^2 + xy + 2y^3 = 4 at the point (-2,1)