_0^ ^2 x ,dx is equal to - Vidyadip

MCQ

$\int_0^\pi {{{\sin }^2}x\,dx} $ is equal to

A
$\pi $
✓
$\frac{\pi }{2}$
C
$0$
D
None of these

✓

Answer

Correct option: B.

$\frac{\pi }{2}$

b
(b) $I = \int_0^\pi {{{\sin }^2}x\,dx = 2\int_0^{\pi /2} {{{\sin }^2}x\,dx} } $,

$\{\because \,\,\int_{0}^{2a}{f(x)=2\int_{0}^{a}{f(a-x)dx}}$, if $f(2a - x) = f(x) \}$

$I = 2 \times \frac{1}{2} \times \frac{\pi }{2} = \frac{\pi }{2}$.

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

There are $3$ bags which are known to contain $2$ white and $3$ black balls; $4$ white and $1$ black balls and $3$ white and $7$ black balls respectively. A ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is

The area of the region $($in square units$)$ bounded by the curve $x^2 = 4y$, line $x = 2$ and $x-$axis is:

What is the value of $\int_{0}^{\frac{\pi}{2}}\frac{\sin\text{x}-\cos\text{x}}{1+\sin\text{x}\cos\text{x}}\text{dx}?$

The number of binary operation that can be defined on a set of 2 elements is:

If $\int {\frac{{\cos 4x + 1}}{{\cot x - \tan x}}} dx = k\,\,\cos 4x + c$ then

Let $\overrightarrow{\mathrm{OA}}=2 \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{OB}}=6 \overrightarrow{\mathrm{a}}+5 \overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{OC}}=3 \overrightarrow{\mathrm{b}}$, where $O$ is the origin. If the area of the parallelogram with adjacent sides $\overrightarrow{\mathrm{OA}}$ and $\overrightarrow{\mathrm{OC}}$ is $15$ sq. units, then the area (in sq. units) of the quadrilateral $\mathrm{OABC}$ is equal to :

If $\frac{\text{dy}}{\text{dx}}=3$ then y is equal to:

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

Complete set of values of $'m'$ for which function $f(x) = {e^{\sin x}} + 2m\sin x + 1$ is increasing $\forall x \in \left( {0,\frac{\pi }{2}} \right)$ , is

The eqution of the plane which cute equal intercepts of unit length on the coordinate axes is: