Questions from General Calculus

Q: Find the area of the region bounded by the parabola y =

Find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at (1, 1), and the x-axis.

Q: Find the number b such that the line y = b divides

Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 4 into two regions with equal area.

Q: (a) Find the number a such that the line x

(a) Find the number a such that the line x − a bisects the area under the curve / (b) Find the number b such that the line y = b bisects the area in part (a).

Q: Find the values of c such that the area of the region

Find the values of c such that the area of the region bounded by the parabolas /

Q: Suppose that /. For what value of c is the area of

Suppose that /. For what value of c is the area of the region enclosed by the curves y = cos x, / equal to the area of the region enclosed by the curves /

Q: Sketch the region enclosed by the given curves. Decide whether to

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the reg...

Q: For what values of m do the line y = mx and

For what values of m do the line y = mx and the curve / enclose a region? Find the area of the region.

Q: The base of S is a circular disk with radius r.

The base of S is a circular disk with radius r. Parallel cross sections perpendicular to the base are isosceles triangles with height h and unequal side in the base. (a) Set up an integral for the vol...

Q: (a) Set up an integral for the volume of a

(a) Set up an integral for the volume of a solid torus (the donut-shaped solid shown in the figure) with radii r and R. (b) By interpreting the integral as an area, find the volume of the torus.

Q: Solve Example 9 taking cross-sections to be parallel to the

Solve Example 9 taking cross-sections to be parallel to the line of intersection of the two planes.