Question

use a geometry formula to find the exact value of the definite integral

2x dx on the inteval [a,b]

Step 1

As a first step let's plot the graph y = 2x and the line x = a and x = b. The line is blue is the plot of y = 2x and those in red are plots of x = a and x = b

The definite integral of 2x dx on the inteval [a,b] = Area under the line y = 2x from x = a to x = b

= Area of the trapezium = ABCD = 1/2 x Sum of the parallel sides AD & CD x distance between the parallel sides

= 1/2 x (AD + BC) x AB

Step 2

AB = b - a

AD = value of y when x is a = 2x = 2a

BC...

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