How do you evaluate the definite integral int2xdx from [0,1]?
1 Answer
Nov 15, 2016
1 square unit
Explanation:
You can solve this many ways:
-
(easiest)Think of it geometrically, as a line
y=2x , and find the area under the curve from0 to1 using the area of a triangle formula -
(easy)Use a fundamental theorem of calculus, and say that if
f(x)=2x , andF(x) is the antiderivative off(x) , thenint_0^1 (2x)dx=F(1)-F(0) -
(hard)Use Riemann sums to find the area under the curve from
0 to1 using an infinite number of rectangles
Method
Method 2:
Let