Integration Reduction Formulas Quiz

Which of the following is a reduction formula?

• ∫x dx = x²/2 + C

• ∫sinⁿx dx = -sinⁿ⁻¹x cos x / n + (n-1)/n ∫sinⁿ⁻²x dx

• ∫dx/x = ln|x| + C

• ∫e^x dx = e^x + C

Reduction formulas are mainly used to evaluate integrals involving:

• Rational functions

• Exponential functions

• Repeated powers of a function

• Constant functions

The reduction formula for ∫xⁿ e^x dx is based on:

• Integration by parts

• Substitution

• Partial fractions

• Direct integration

Bernoulli's formula is an extension of:

• Chain rule

• L'Hôpital's Rule

• Integration by parts

• Leibniz rule

The formula for ∫xⁿ log x dx involves:

• Trigonometric substitution

• Integration by parts

• Partial fractions

• Change of limits

Which of the following functions can be integrated using a reduction formula?

• ln(x)

• sin(x)

• sinⁿ(x)

• x² + 3x + 1

The standard reduction formula for ∫cosⁿx dx is:

• n ∫cosⁿ⁻¹x dx

• cosⁿx / n

• (n-1)/n ∫cosⁿ⁻²x dx

• ∫cos x dx

What is ∫x⁴ e^x dx best evaluated by?

• Substitution

• Rewriting as power series

• Integration by parts with reduction

• Change of variable to log

Bernoulli's formula is used when:

• One function is easily integrable and the other is differentiable

• Both functions are trigonometric

• Both functions are logarithmic

• None of the above

The integration of ∫xⁿ sin x dx is simplified using:

• Partial fractions

• Bernoulli's formula

• Rationalization

• Trapezoidal Rule