Lösung 2.1:1b
Aus Online Mathematik Brückenkurs 2
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Version vom 10:14, 11. Mär. 2009
The graph of the function \displaystyle y=2x+1 is a straight line which cuts the y-axis at \displaystyle y=1 and has slope 2.
The integral's value is the area under the straight line and between \displaystyle x=0 and \displaystyle 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
| \displaystyle \begin{align}
\int\limits_{0}^{1} (2x+1)\,dx &= \text{(area of the square)} + \text{(area of the triangle)}\\ &= 1\cdot 1 + \frac{1}{2}\cdot 1\cdot 2 = 2\,\textrm{.} \end{align} |
