_ - 2 ^2 |1 - x^2 | ,dx = - Vidyadip

MCQ

$\int_{ - 2}^2 {|1 - {x^2}|\,dx = } $

A
$2$
✓
$4$
C
$6$
D
$8$

✓

Answer

Correct option: B.

$4$

b
(b) $\int_{-2}^{-1}{|1-{{x}^{2}}|\,dx+\int_{-1}^{1}{|1-{{x}^{2}}|\,dx-\int_{1}^{2}{|1-{{x}^{2}}|\,dx}}}$

$ + \int_1^2 {|1 - {x^2}|dx} $

$= - \int_{ - 2}^{ - 1} {(1 - {x^2})\,dx + \int_{ - 1}^1 {(1 - {x^2})\,dx - \int_1^2 {(1 - {x^2})\,dx} } } $

$= \frac{4}{3} + \frac{4}{3} + \frac{4}{3} = 4.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int_0^{2 \pi} \operatorname{cosec}^7 x d x=$

The line $\frac{{x - 2}}{1} = \frac{{y - 3}}{1} = \frac{{z - 4}}{{ - k}}$ and $\frac{{x - 1}}{k} = $ $\frac{{y - 4}}{2} = \frac{{z - 5}}{1}$ are coplanar, if

The direction cosines of a line which is equally inclined to axes, is given by:

If $(n - m)$ is odd and $|m|\, \ne \,|n|,$ then $\int_0^\pi {\cos mx\sin nx} \,dx$ is

The projections of a line segment on $x, y$ and $z$ axes are $12, 4$ and $3$ respectively. The length and direction cosines of the line segment are:

There are $50$ apple trees in an orchard. Each tree produces $800$ apples. For each additional tree planted in the orchard, the output per additional tree drops by $10$ apples. Number of trees that should be added to the existing orchard for maximising the output of the trees, is

Area bounded by curves $x = \sqrt {2 - {y^2}} $ and $\left| x \right| = \left| y \right|,$ is -

If $\sin ({\cot ^{ - 1}}(x + 1) = \cos ({\tan ^{ - 1}}x)$, then $ x =$

If $ A $ is a non- singular matrix, then $ A(adj A) =$

${d \over {dx}}\log |x|{\rm{ }} = ......,(x \ne 0)$