Function, Its Antiderivative, and Definite Integral | math4u.vsb.cz

Submitted by michaela.bailova on Fri, 09/13/2024 - 16:53

SubArea:

Definite integral

Project ID:

7500020146

Question:

Create matching triples consisting of the graph of a function

f

, its antiderivative

F

, and the definite integral

\int_{0}^{1} f (x) d x

.

Header 1:

Graph of a function

f

Header 2:

Antiderivative

F

Header 3:

Definite integral

\int_{0}^{1} f (x) d x

Image 11:

Text 21:

F (x) = x

Text 31:

\int_{0}^{1} f (x) d x = 1

Image 12:

Text 22:

F (x) = \frac{x^{2}}{2}

Text 32:

\int_{0}^{1} f (x) d x = \frac{1}{2}

Image 13:

Text 23:

F (x) = x - \frac{x^{2}}{4}

Text 33:

\int_{0}^{1} f (x) d x = \frac{3}{4}

Image 14:

Text 24:

F (x) = \frac{x^{3}}{3}

Text 34:

\int_{0}^{1} f (x) d x = \frac{1}{3}

Image 15:

Text 25:

F (x) = 2 x - \frac{x^{3}}{6}

Text 35:

\int_{0}^{1} f (x) d x = \frac{11}{6}

Image 16:

Text 26:

F (x) = x^{2} + \frac{x^{3}}{3}

Text 36:

\int_{0}^{1} f (x) d x = \frac{4}{3}

Workflow:

publish