Main content
Unit 1: Integrals
3,700 possible mastery points
Mastered
Proficient
Familiar
Attempted
Not started
Quiz
Unit test
About this unit
The definite integral of a function gives us the area under the curve of that function. Another common interpretation is that the integral of a rate function describes the accumulation of the quantity whose rate is given. We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. The fundamental theorem of calculus ties integrals and derivatives together and can be used to evaluate various definite integrals.Learn
Practice
- Left & right Riemann sumsGet 3 of 4 questions to level up!
- Over- and under-estimation of Riemann sumsGet 3 of 4 questions to level up!
- Midpoint & trapezoidal sumsGet 3 of 4 questions to level up!
Learn
Practice
- Summation notationGet 3 of 4 questions to level up!
Learn
Practice
- Riemann sums in summation notationGet 3 of 4 questions to level up!
Learn
Practice
- Definite integral as the limit of a Riemann sumGet 3 of 4 questions to level up!
Learn
Practice
- Functions defined by definite integrals (accumulation functions)Get 3 of 4 questions to level up!
- Finding derivative with fundamental theorem of calculusGet 3 of 4 questions to level up!
- Finding derivative with fundamental theorem of calculus: chain ruleGet 3 of 4 questions to level up!
Learn
Practice
- Finding definite integrals using area formulasGet 3 of 4 questions to level up!
- Finding definite integrals using algebraic propertiesGet 3 of 4 questions to level up!
- Definite integrals over adjacent intervalsGet 3 of 4 questions to level up!
Learn
Practice
- The fundamental theorem of calculus and definite integralsGet 3 of 4 questions to level up!
- Antiderivatives and indefinite integralsGet 3 of 4 questions to level up!
Learn
Practice
- Reverse power ruleGet 3 of 4 questions to level up!
- Reverse power rule: negative and fractional powersGet 3 of 4 questions to level up!
- Reverse power rule: sums & multiplesGet 3 of 4 questions to level up!
- Reverse power rule: rewriting before integratingGet 3 of 4 questions to level up!
Learn
Practice
- Indefinite integrals: eˣ & 1/xGet 3 of 4 questions to level up!
- Indefinite integrals: sin & cosGet 3 of 4 questions to level up!
- Integrating trig functionsGet 5 of 7 questions to level up!
Learn
Practice
- Definite integrals: reverse power ruleGet 3 of 4 questions to level up!
- Definite integrals: common functionsGet 3 of 4 questions to level up!
- Definite integrals of piecewise functionsGet 3 of 4 questions to level up!
Learn
Practice
- 𝘶-substitution: defining 𝘶Get 3 of 4 questions to level up!
- 𝘶-substitution: indefinite integralsGet 3 of 4 questions to level up!
- 𝘶-substitution: definite integralsGet 3 of 4 questions to level up!
Learn
Practice
- Integration using long divisionGet 3 of 4 questions to level up!
- Integration using completing the squareGet 3 of 4 questions to level up!
Learn
Practice
- Trigonometric substitutionGet 3 of 4 questions to level up!
Learn
Practice
- Integration by partsGet 3 of 4 questions to level up!
- Integration by parts: definite integralsGet 3 of 4 questions to level up!
Practice
- Integration with partial fractionsGet 3 of 4 questions to level up!
Up next for you:
Level up on all the skills in this unit and collect up to 3700 Mastery points!