Derivatives and Integrals

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BrightestChrysanthemum
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8 Questions

What is the process of finding the integral of a function called?

Integration

What is the result of an indefinite integral also known as?

Antiderivative

What does the definite integral represent?

Area under the curve

Which rule allows for the integration of a product of two functions?

Integration by parts

Qual es le resultato del integration indefinite de 1/x?

ln|x| + C

Qual es le integral definite de sin(x) de 0 a π?

0

Qual es le integral definite de tan(x) de π/4 a π/2?

1

Qual es le integral definite de sec(x) de 0 a π/2?

1

Study Notes

Integration

  • The process of finding the integral of a function is called integration.
  • The result of an indefinite integral is also known as the antiderivative.

Definite Integral

  • The definite integral represents the area between the graph of a function and the x-axis over a specific interval.

Integration Rules

  • The product rule allows for the integration of a product of two functions.

Integration of Specific Functions

  • The result of the indefinite integral of 1/x is the natural logarithm.
  • The definite integral of sin(x) from 0 to π is 2.
  • The definite integral of tan(x) from π/4 to π/2 is 1.
  • The definite integral of sec(x) from 0 to π/2 is 1.

Test your knowledge of derivatives and integrals with this quiz, covering various anti-derivative formulas and integral calculations for different functions.

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