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8. Application and integration — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths8. Application and integration1 Mark
MCQ
If $f(x)$ is conitinuous , increasing and an odd function such that $\int\limits_{ - 1}^4 {f\left( x \right)} \,dx = 10$ and $\int\limits_0^1 {f\left( x \right)} \,dx = \frac{3}{2}$ then the area bounded by $y =f(x)$, $x -$ axis in between the ordinates $x = -4$ and $x = 4$ is
  • ✓
    $23$
  • B
    $19$
  • C
    $20$
  • D
    $\frac{{23}}{2}$
✓

Answer

Correct option: A.
$23$
a
$\int\limits_{ - 1}^4 {f\left( x \right)} dx = 10$

$ \Rightarrow \int\limits_{ - 1}^0 {f\left( x \right)} dx + \int\limits_0^4 {f\left( x \right)dx}  = 10$

$ \Rightarrow  - \int\limits_0^1 {f\left( x \right)} dx + \int\limits_0^4 {f\left( x \right)dx}  = 10$

$ \Rightarrow \int\limits_0^4 {f\left( x \right)dx}  = \frac{{23}}{2}$

Therfore Required Area $=23$

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