Questions from General Calculus

Q: Determine the integrals by making appropriate substitutions. ∫ (x

Determine the integrals by making appropriate substitutions. ∫ (x – 3)/(1 - 6x + x2)2 dx

Q: Find the area under the graph of y = 1/x2

Find the area under the graph of y = 1/x2 for x ≥ 2.

Q: Find the area under the graph of y = (x +

Find the area under the graph of y = (x + 1)-2 for x ≥ 0.

Q: Find the area under the graph of y = e-x

Find the area under the graph of y = e-x/2 for x ≥ 0.

Q: Find the area under the graph of y = 4 e-

Find the area under the graph of y = 4 e-4x for x ≥ 0.

Q: Find the area under the graph of y = (x +

Find the area under the graph of y = (x + 1)-3/2 for x ≥ 3.

Q: Find the area under the graph of y = (2x +

Find the area under the graph of y = (2x + 6)-4/3 for x ≥ 1. (See Fig. 8.) Figure 8:

Q: Show that the region under the graph of y = (14x

Show that the region under the graph of y = (14x + 18)-4/5 for x ≥ 1 cannot be assigned any finite number as its area. (See Fig. 9.) Figure 9:

Q: Show that the region under the graph of y = (x

Show that the region under the graph of y = (x - 1)-1/3 for x ≥ 2 cannot be assigned any finite number as its area.

Q: Evaluate the following improper integrals whenever they are convergent. ∫

Evaluate the following improper integrals whenever they are convergent. ∫1 ∞ x3 dx