Questions from General Calculus

Q: Evaluate the integral. /

Evaluate the integral.

Q: Evaluate the integral. /

Evaluate the integral.

Q: Evaluate the integral. /

Evaluate the integral.

Q: Evaluate the integral. /

Evaluate the integral.

Q: Evaluate the integral. /

Evaluate the integral.

Q: Evaluate the integral. /

Evaluate the integral.

Q: For which of the following series is the Ratio Test inconclusive (

For which of the following series is the Ratio Test inconclusive (that is, it fails to give a definite answer)?

Q: Evaluate the integral. /

Evaluate the integral.

Q: (a) Use trigonometric substitution to show that /

(a) Use trigonometric substitution to show that (b) Use the hyperbolic substitution x = a sinh t to show that These formulas are connected by Formula 3.11.3.

Q: Evaluate / (a) by trigonometric substitution.

Evaluate (a) by trigonometric substitution. (b) by the hyperbolic substitution x = a sinh t.