Question

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Answer 1

Each of those definite integrals are expressions for the area underneath the curve of the function. If you look at the curve, there are two parts - one above the x axis and one below the x axis. The first part has positive area and the second part has negative area.

Now, since all of these integrals start from 0, with f(0)=0, we just need to think about what endpoint would give use the largest area.

Choice (A) stops at 1 and f(1) is positive, so it would have some positive number for the area.

Choice (B) stops at 2, with f(2)=0, so it would have more positive area than if we had stopped at 1.

Choice (C) stops at 3, with f(3) being negative, which means that going from 2 to 3 introduces some negative area, so choice (C) is smaller than choice (B). In fact, the other two choices lead to even more negative area being included, so those choices are even less than choice (C). Therefore, the integral in choice (B) gives us the largest value.

Answer 2

oh okay that makes a lot of sense thank you!