The function f x is defined as - x - x - for -1- x - 2- The area under the curve y - f x isA- 1B- 2C- 4D- 3

The correct option is B 2 nbsp; A_1=12× 1×1=12 A_2=12× 1×1=12 A_3= 1×1=1 nbsp; ∴Required area=12+12+1=2 sq. units nbsp; nbsp; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Graph of [x]

The function ...

Question

The function $f (x)$ is defined as $| [x] x |$ for $- 1 < x \leq 2$ .
The area under the curve $y = f (x)$ is

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2$

$A_{1} = \frac{1}{2} \times 1 \times 1 = \frac{1}{2}$
$A_{2} = \frac{1}{2} \times 1 \times 1 = \frac{1}{2}$
$A_{3} = 1 \times 1 = 1$

$∴ Required area = \frac{1}{2} + \frac{1}{2} + 1 = 2 sq. units$

Suggest Corrections

Similar questions

Q. The function

f (x)

is defined as

| [x] x |

for

- 1 < x \leq 2

.
The area under the curve

y = f (x)

Consider the function f : R $\to$ R, defined as $⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} x^{2} - x + 3, x ϵ (- \infty, 3) \cap Q x + a, x ϵ (- \infty, 2) - Q 2^{x} + 1, x ϵ (2, 3) - Q 9 t a n (\frac{π x}{12}), x ϵ [3, 6] \end{matrix}$

If f(x) is continuous at x = 2 then the value of a is

Q. The values of

x

for which the function

f (x) = \frac{x^{2} + x + 1}{x^{2} - 7 x + 12}

is not defined, is

The maximum value of the function $f (x) = - | x + 1 | + 3$ is

Q. The range of the function

f (x) = \frac{2 + x}{2 - x}, x \neq 2

Join BYJU'S Learning Program

The function f(x) is defined as |[x]x| for −1<x≤2. The area under the curve y=f(x) is

The correct option is B 2 A1=12×1×1=12 A2=12×1×1=12 A3=1×1=1 ∴Required area=12+12+1=2 sq. units

The function $f (x)$ is defined as $| [x] x |$ for $- 1 < x \leq 2$ .
The area under the curve $y = f (x)$ is

The correct option is B $2$

$A_{1} = \frac{1}{2} \times 1 \times 1 = \frac{1}{2}$
$A_{2} = \frac{1}{2} \times 1 \times 1 = \frac{1}{2}$
$A_{3} = 1 \times 1 = 1$

$∴ Required area = \frac{1}{2} + \frac{1}{2} + 1 = 2 sq. units$