What is the integral of 2x from 0 to 5?

The definite integral of 2x from 0 to 5 as the area under the line y = 2x: the antiderivative x² gives 5² − 0² = 25, the area of a triangle with base 5 and height 10.

Step-by-step explanation

1. We want to find the area under the curve f(x) = 2x from x = 0 to x = 5. This is represented by the definite integral of 2x dx.
2. The definite integral represents the area between the function and the x-axis. For f(x) = 2x, this area forms a right triangle.
3. Using the Power Rule for integration, the antiderivative of 2x is x squared. We evaluate this from the lower limit 0 to the upper limit 5.
4. Substitute the upper limit 5 and the lower limit 0 into the expression. This gives us 5 squared minus 0 squared.
5. Finally, calculating the values gives us 25 minus 0, which equals 25. Geometrically, this is the area of a triangle with base 5 and height 10.

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