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Lösung 2.1:1b

Aus Online Mathematik Brückenkurs 2

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The value of the integral is
The value of the integral is
-
{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
\int\limits_{0}^{1} (2x+1)\,dx
\int\limits_{0}^{1} (2x+1)\,dx
&= \text{(area of the square)} + \text{(area of the triangle)}\\
&= \text{(area of the square)} + \text{(area of the triangle)}\\
&= 1\cdot 1 + \frac{1}{2}\cdot 1\cdot 2 = 2\,\textrm{.}
&= 1\cdot 1 + \frac{1}{2}\cdot 1\cdot 2 = 2\,\textrm{.}
\end{align}</math>}}
\end{align}</math>}}

Version vom 12:57, 10. Mär. 2009

The graph of the function y=2x+1 is a straight line which cuts the y-axis at y=1 and has slope 2.

The integral's value is the area under the straight line and between x=0 and x=1.

We can divide up the region under the graph into a square and rectangle,

and then add up the area to obtain the total area.

The value of the integral is

10(2x+1)dx=(area of the square)+(area of the triangle)=11+2112=2.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_2.1:1b“