Discussion
The value of \(\int_{-1}^{1}|x - 3|\,dx\) is equal to
Answer: B
The integral is 6.
On \([-1, 1]\), \(x - 3 \lt 0\), so \(|x - 3| = 3 - x\):
\[ \begin{aligned} \int_{-1}^{1}(3 - x)\,dx \\ &= \left[3x - \frac{x^{2}}{2}\right]_{-1}^{1} \\ &= 2.5 - (-3.5) \\ &= 6 \end{aligned} \]
An integral of an absolute value cannot be negative, which rules out \(-5\) and \(-6\); 0 and 5 come from mishandling the \(x\) term.
Geometrically it is the area of a trapezium with parallel sides 4 and 2 (the values of \(3 - x\) at \(-1\) and 1) and width 2: \(\frac{4 + 2}{2} \times 2 = 6\).
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development