Definite Integration
Integration with Absolute Values
Grade 12
Question:
<p>If <span>\(m = \int_0^{\pi/2} \frac{|\sin x|}{x + 1} dx\)</span> and <span>\(n = \int_0^{\pi/2} \frac{|\sin x|}{x + 1} dx\)</span> (where <span>\([\cdot]\)</span> = G.I.F.), then</p>
<p>(A) m = n</p>
<p>(B) m = –n</p>
<p>(C) m = 2n</p>
<p>(D) None of these</p>
Step-by-Step Solution
Key Concept: Apply the property that integrals with absolute value functions can be related through symmetry properties.
<p>Use properties of absolute value functions and symmetry in definite integration to establish the relationship between m and n.</p>
Correct Answer: B