Questions from General Calculus

Q: Evaluate the integral. f32 1/x2 – 1,

Evaluate the integral. f32 1/x2 – 1, dx

Q: Evaluate the integral. f x2 + 2x – 1/

Evaluate the integral. f x2 + 2x – 1/ x3 – x, dx

Q: First make a substitution and then use integration by parts to evaluate

First make a substitution and then use integration by parts to evaluate the integral.

Q: Some computer algebra systems have commands that will draw approximating rectangles and

Some computer algebra systems have commands that will draw approximating rectangles and evaluate the sums of their areas, at least if is a left or right endpoint. (For instance, in Maple use leftbox,...

Q: Water in an open bowl evaporates at a rate proportional to the

Water in an open bowl evaporates at a rate proportional to the area of the surface of the water. (This means that the rate of decrease of the volume is proportional to the area of the surface.) Show t...

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: Evaluate the integral. f 2x2 + 5/ (x2

Evaluate the integral. f 2x2 + 5/ (x2 + 1) (x2 + 4), dx

Q: Evaluate the integral. f x3 + x2 + 2x +

Evaluate the integral. f x3 + x2 + 2x + 1/ (x2 + 1) (x2 + 2), dx

Q: Evaluate the integral. f x2 – x + 6/

Evaluate the integral. f x2 – x + 6/ x3 + 3x, dx

Q: Use long division to evaluate the integral. f x/

Use long division to evaluate the integral. f x/x – 6, dx