If f(x) is conitinuous , increasing and an odd function such that… - Vidyadip

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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