Questions from General Calculus

Q: Find the area of the region bounded by the hyperbola 9x2 -

Find the area of the region bounded by the hyperbola 9x2 - 4y2 = 36 and the line x = 3.

Q: Evaluate the integral / Graph the integrand and its indefinite

Evaluate the integral Graph the integrand and its indefinite integral on the same screen and check that your answer is reasonable.

Q: Find the volume of the solid obtained by rotating about the x

Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the curves /

Q: Find the volume of the solid obtained by rotating about the line

Find the volume of the solid obtained by rotating about the line x = 1 the region under the curve /

Q: (a) Use trigonometric substitution to verify that /

(a) Use trigonometric substitution to verify that (b) Use the figure to give trigonometric interpretations of both terms on the right side of the equation in part (a).

Q: For which positive integers k is the following series convergent?

For which positive integers k is the following series convergent?

Q: The parabola y = 1 2 x2 divides the

The parabola y = 1 2 x2 divides the disk x2+y2 < 8 into two parts. Find the areas of both parts.

Q: A torus is generated by rotating the circle x2 + (y

A torus is generated by rotating the circle x2 + (y-R)2 = r2 about the x-axis. Find the volume enclosed by the torus.

Q: A charged rod of length L produces an electric field at point

A charged rod of length L produces an electric field at point P(a, b) given by where / is the charge density per unit length on the rod and «0 is the free space permittivity (see the figu...

Q: Find the area of the crescent-shaped region (called a

Find the area of the crescent-shaped region (called a lune) bounded by arcs of circles with radii r and R.