Sketch a graph of y = 2x on [-1, 2] and use geometry to find the exact value of function given int_{-1}^{2} 2x dx

Falak Kinney 2021-01-31 Answered
Sketch a graph of y=2xon[1,2] and use geometry to find the exact value of function given
122x dx
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Aamina Herring
Answered 2021-02-01 Author has 85 answers

Let's sketch the graph of the following function:
y=2x
on [1,2]
image
We can use several methods to find the value of the given expression either by Riemann Sum, or by another sum methods where we need to divide this interval into equal sub-intervals : But we use the easiest method that is we can simply integrate the following expression using the property of integration and then apply the limits:
The given expression is :
122x dx
Let's integrate the following expression:
122x dx=212xdx
=2[x22]12
=[x2]12
=[(2)2(1)2]
=[41]=3 Hence, the value of the given expression is : 3

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