Mathematics Quiz: Integration Methods
Integration by reverse power rule rewriting and properties of integrals reverse chain rule (substitution)
- 1.Which statement best describes the meanings of definite and indefinite integrals?
- A.
Definite and indefinite integrals represent areas under curves. Definite integrals are for a specific interval, while indefinite integrals are accumulation functions.
- B.
Definite integrals represent backwards differentiation while indefinite integrals represent limits of Riemann sums.
- C.
Definite integrals represent areas under curves while indefinite integrals represent families of antiderivatives.
- D.
Definite integrals represent families of antiderivatives while indefinite integrals represent specific antiderivatives.
- 2.
![Which plan(s) could be followed to integrate - ProProfs]( "Which plan(s) could be followed to integrate")
Which plan(s) could be followed to integrate- A.
First rewrite the integrand in general form and then apply the power rule to each term.
- B.
Raise the power to 4 and then divide by 4.
- C.
Distribute the exponent to the two terms and then apply the power rule to each term.
- D.
Substitute u=1–x and then apply the power rule to integrate u^3.
- 3.
![Now carry out this integration:
Is the derivative of your result equivalent to the integrand? - ProProfs]( "Now carry out this integration:
Is the derivative of your result equivalent to the integrand?")
Now carry out this integration: Is the derivative of your result equivalent to the integrand?- A.
Yes
- B.
No
- 4.
![What would be a useful substitution to perform this integration? - ProProfs]( "What would be a useful substitution to perform this integration?")
What would be a useful substitution to perform this integration?- A.
U=2x^2
- B.
W=x^2
- C.
Z=4+3x^3
- D.
M=(4+3x^3)^6
- 5.
![Now carry out this integration:
Is the derivative of your result equivalent to the integrand? - ProProfs]( "Now carry out this integration:
Is the derivative of your result equivalent to the integrand?")
Now carry out this integration: Is the derivative of your result equivalent to the integrand?- A.
Yes
- B.
No
- 6.Which two scientists were involved in the discovery of "the Fundamental Theorem of Calculus?"
- A.
Sir Isaac Newton
- B.
Albert Einstein
- C.
Gottfried Wilhelm Leibniz
- D.
Srinivasa Ramanujan
- 7.Who introduced the notation for the indefinite integral?
- A.
Jacob Bernoulli
- B.
Joseph Fourier
- C.
Gottfried Leibniz
- D.
Georg Riemann
.png "Now carry out this integration:
Is the derivative of your result equivalent to the integrand?")
.png "Now carry out this integration:
Is the derivative of your result equivalent to the integrand?")
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