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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_{-1}^1 x^{17} \cos ^4 x d x=$
  • A
    -2
  • B
    -1
  • ✓
    $0$
  • D
    2
✓

Answer

Correct option: C.
$0$
(C)
Let $f (x)=x^{17} \cos ^4 x$
$\begin{array}{l}\therefore \quad f (-x)=(-x)^{17}\{\cos (-x)\}^4=- f (x) \\ \therefore \quad f (x) \text { is an odd function. } \\ \therefore \quad \int_{-1}^1 x^{17} \cos ^4 x d x=0\end{array}$

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