Find the area of the region under the graph of f on [a, b]. $f(x)=x^{2}-2 x+2 ; \quad[-1,2]$
A) -3
B) -6
C) 6
D) 3

Name: Find the area of the region under the graph of f on [a, b]. $f(x)=x^{2}-2 x+2 ; \quad[-1,2]$ A) -3 B) -6 C) 6 D) 3
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Question

Quizplus · Accepted Answer

To find the area under the graph of f, we need to integrate f(x) from -1 to 2:

$$\int_{-1}^{2}(x^{2}-2x+2) dx=\left[\frac{x^{3}}{3}-x^{2}+2x\right]_{-1}^{2}=6$$

Therefore, the area of the region under the graph of f on [a, b] is 6, and the best choice is C.

Find the Area of the Region Under the Graph of F