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Application of Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Integrals1 Mark
MCQ
Area bounded by the curvey $\text{y}=\text{x}+\sin\text{x}$ and its inverse function between the ordinates $\text{x}=0$ and $\text{x}=2\pi$ is:
  • A
    $8\pi\text{ sqp}.$ units
  • B
    $4\pi\text{ sq}.$ units
  • ✓
    $8\pi\text{ sq}.$ units
  • D
    $3\pi\text{ sq}.$ units
✓

Answer

Correct option: C.
$8\pi\text{ sq}.$ units
Inverse function is the mirror image with respect to $y = x$
Then area bounded by $\text{x}+\sin\text{x}$ and its inverse function is
$=4\int\limits^\pi_0(\text{x}+\sin\text{x}-\text{x})\text{ dx}=8$

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