Assertion (A): $\int_{-1}^{1} x\,dx = 0$ , so the line $y = x$ encloses no area with the $x$ -axis between $x = -1$ and $x = 1$ .
Reason (R): A definite integral counts area below the $x$ -axis as negative.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The two triangles each have area $\frac{1}{2}$ , so the region's area is 1, not 0: A is false.
R is true, and it is exactly why the integral is 0 while the area is not.

Concept: Integral and area are not the same
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsArea under a simple curve

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Ten questions from Definite Integrals & Area, at your own pace.

Assertion (A): ∫−11x dx=0\int_{-1}^{1} x\,dx = 0∫−11​xdx=0, so the line y=xy = xy=x encloses no area with the xxx-axis between x=−1x = -1x=−1 and x=1x = 1x=1.Reason (R): A definite integral counts area below the xxx-axis as negative.

Explanation

Assertion (A): $\int_{-1}^{1} x\,dx = 0$ , so the line $y = x$ encloses no area with the $x$ -axis between $x = -1$ and $x = 1$ .
Reason (R): A definite integral counts area below the $x$ -axis as negative.