Questions from General Calculus

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

Determine the integrals by making appropriate substitutions. ∫ (1 + ln x)3 / x dx

Q: Evaluate the following integrals using techniques studied thus far. ∫

Evaluate the following integrals using techniques studied thus far. ∫ x sec2 (x2 + 1) dx

Q: Evaluate the following integrals using techniques studied thus far. ∫

Evaluate the following integrals using techniques studied thus far. ∫ ln x / x5 dx

Q: Evaluate the following integrals using techniques studied thus far. ∫

Evaluate the following integrals using techniques studied thus far. ∫ (x e2x + x2) dx

Q: Evaluate the following integrals using techniques studied thus far. ∫

Evaluate the following integrals using techniques studied thus far. ∫ (x3/2 + ln 2x) dx

Q: Evaluate the following integrals using techniques studied thus far. ∫

Evaluate the following integrals using techniques studied thus far. ∫ (x ex2 - 2x) dx

Q: Evaluate the following integrals using techniques studied thus far. ∫

Evaluate the following integrals using techniques studied thus far. ∫ (x2 - x sin 2x) 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/√(x + 9). Find the expression for the function f (x) whose graph passes through (0, 2). 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 x / ex/3. Find the expression for the function f (x) whose graph passes through (0, 6). Figure 2:

Q: Evaluate ∫x ex (x + 1)2 dx

Evaluate ∫x ex (x + 1)2 dx using integration by parts.