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Integrals and it's Applications — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsIntegrals and it's Applications1 Mark
MCQ
Find the value of $\int_1^4|x-5| d x$.
  • A
    2
  • ✓
    $\frac{15}{2}$
  • C
    $\frac{2}{15}$
  • D
    15
✓

Answer

Correct option: B.
$\frac{15}{2}$
(B)$\frac{15}{2}$
$\int_1^4|x-5| d x=\int_1^4-(x-5) d x$
$=-\frac{1}{2}\left[(x-5)^2\right]_1^4$
$\int_1^4|x-5| d x=-\frac{1}{2}[1-16]=\frac{15}{2}$

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