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APPLICATION OF INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF INTEGRALS1 Mark
Question
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:

  1. $8\pi\text{ sqp}.\text{units}$

  2. $4\pi\text{ sq}.\text{units}$

  3. $8\pi\text{ sq}.\text{units}$

  4. $3\pi\text{ sq}.\text{units}$

✓

Answer

  1. $8\pi\text{ sq}.\text{units}$

Solution:

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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