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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int_{-\pi}^\pi x^{10} \sin ^7 x d x$
  • A
    1
  • B
    2
  • C
    -1
  • ✓
    0
✓

Answer

Correct option: D.
0
(d) : Let $I=\int_{-\pi}^\pi x^{10} \sin ^7 x d x$
Let $f(x)=x^{10} \sin ^7 x$
and $f(-x)=(-x)^{10}[\sin (-x)]^7=-x^{10} \sin ^7 x=-f(x)$
$\therefore f(x)$ is an odd function.
$\therefore \quad I=\int_{-\pi}^\pi x^{10} \sin ^7 x d x=0$

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