Questions from General Calculus

Q: Determine the integral by making appropriate substitutions. ∫ (ex

Determine the integral by making appropriate substitutions. ∫ (ex + e-x) / (ex - e-x) dx

Q: Determine the integral by making appropriate substitutions. ∫ (1

Determine the integral by making appropriate substitutions. ∫ (1 + e-x)3 / ex dx

Q: Determine the integral by making appropriate substitutions. ∫ 1 /

Determine the integral by making appropriate substitutions. ∫ 1 / (1 + ex) dx

Q: Determine the integral by making appropriate substitutions. ∫ (e2x

Determine the integral by making appropriate substitutions. ∫ (e2x - 1) / (e2x + 1) dx

Q: Figure 1 shows graphs of several functions f (x) whose

Figure 1 shows graphs of several functions f (x) whose slope at each x is x/√(x2 + 9). Find the expression for the function f (x) whose graph passes through (4, 8). Figure 1:

Q: Figure 2 shows graphs of several functions f (x) whose

Figure 2 shows graphs of several functions f (x) whose slope at each x is (2√x + 1)/ √x. Find the expression for the function f (x) whose graph passes through (4, 1...

Q: Determine the integrals by making appropriate substitutions. ∫ (x2

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

Q: Determine the following integrals using the indicated substitution. ∫ (

Determine the following integrals using the indicated substitution. ∫ (x + 5)-1/2 e√(x+5) dx; u = √(x+5)

Q: Determine the following integrals using the indicated substitution. ∫ x4

Determine the following integrals using the indicated substitution. ∫ x4 / (x5 – 7) ln(x5 - 7) dx; u = ln(x5 - 7)

Q: Determine the following integrals using the indicated substitution. ∫ x

Determine the following integrals using the indicated substitution. ∫ x sec2 x2 dx; u = x2