Assertion (A): ∫₋₁^1 x| x | dx = 0. Reason (R): x| x | is an odd function.

Definite Integrals & Area · Question 44 of 71

Question 44

MediumOriginal question

Assertion (A): $\int_{-1}^{1} x\lvert x \rvert\,dx = 0$ .
Reason (R): $x\lvert x \rvert$ is an odd function.

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 A

Correct answer: A

R: $(-x)\lvert -x \rvert = -x\lvert x \rvert$ , so the function is odd. True.
An odd function over $[-1, 1]$ integrates to 0, so A is true because of R.

Concept: Integrals of odd functions over symmetric limits
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsProperties of definite integrals

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Assertion (A): ∫−11x∣x∣ dx=0\int_{-1}^{1} x\lvert x \rvert\,dx = 0∫−11​x∣x∣dx=0.Reason (R): x∣x∣x\lvert x \rvertx∣x∣ is an odd function.

Explanation

Assertion (A): $\int_{-1}^{1} x\lvert x \rvert\,dx = 0$ .
Reason (R): $x\lvert x \rvert$ is an odd function.