Questions from General Calculus

Q: Find the are of the shaded region. /

Find the are of the shaded region.

Q: Evaluate the following definite integrals. ∫5/2 3

Evaluate the following definite integrals. ∫5/2 3 2(2x - 5)14 dx

Q: Evaluate the following definite integrals. ∫2 6 1/

Evaluate the following definite integrals. ∫2 6 1/ √(4x + 1) dx

Q: Evaluate the following definite integrals. ∫0 24x (1

Evaluate the following definite integrals. ∫0 24x (1 + x2)3 dx

Q: Determine the integrals by making appropriate substitutions. ∫ e√

Determine the integrals by making appropriate substitutions. ∫ e√x /√x dx

Q: Divide the interval into n subintervals and list the value of x

Divide the interval into n subintervals and list the value of x and the midpoints x1, .… , xn of the subintervals. -1 ≤ x ≤ 1; n = 4

Q: Divide the interval into n subintervals and list the value of x

Divide the interval into n subintervals and list the value of x and the midpoints x1, .… , xn of the subintervals. -1 ≤ x ≤ 1; n = 4 0 ≤ x ≤ 3; n = 6

Q: Refer to the graph in Fig. 11. Draw the rectangles

Refer to the graph in Fig. 11. Draw the rectangles that approximate the area under the curve from 0 to 8 when using the midpoint rule with n = 4. Figure 11:

Q: Refer to the graph in Fig. 11. Apply the trapezoidal

Refer to the graph in Fig. 11. Apply the trapezoidal rule with n = 4 to estimate the area under the curve. Figure 11:

Q: Approximate the following integrals by the midpoint rule; then, find

Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. ∫0 4 (x2 + 5) dx; n = 2, 4