If _ 0 ^ 2 is equal to: - Vidyadip

MCQ

If $\int\limits_{0}^{\frac{\pi}{2}}\sin\text{x}\cos\text{xdx}$ is equal to:

✓
$\frac{1}{2}$
B
$\frac{1}{4}$
C
$2$
D
$1$

✓

Answer

Correct option: A.

$\frac{1}{2}$

$\int\limits_{0}^{\frac{\pi}{2}}\sin\text{x}\cos\text{xdx}$
$\sin\text{x}=\text{t}\Rightarrow\cos\text{xdx}=\text{dt}$
$\text{x}\Rightarrow0\Rightarrow\frac{\pi}{2}$
$\int\limits_{0}^{\frac{\pi}{2}}\text{tdt}$
$\Rightarrow\frac{\text{t}^2}{2}\mid^1_0$
$\Rightarrow\frac{1}{2}-0=\frac{1}{2}$

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 INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

ABCD is a parallelogram with AC and BD as diagonals. Then, $\overrightarrow{\text{AC}}-\overrightarrow{\text{BD}}=$

The function $f\left( x \right) = {\tan ^{ - 1}}\left( {\sin x + \cos x} \right)$ is an increasing function in

If the function $f(x) = \left\{ \begin{array}{l}
{\tan ^{ - 1}}x;x < 1\\
{\sec ^{ - 1}}x + \lambda ;x \ge 1
\end{array} \right.$ has local minima at $x = 1$, then range of $\lambda$ is-

The differential equation $\frac{\text{dx}}{\text{dx}}=\frac{1}{\text{ax}+\text{by}+\text{c}},$ where a, b, c are all non zero real numbers, is:

A fair die is tossed eight times. The probability that a third six is observed in the eight throw is:

If $A$ is a square matrix of order $4$ and $B = AdjA$, where $|B| = 27$, then value of $|A^{-1}Adj(3AB)|$ is, (where $A^{-1}$ denotes inverse of matrix $A$ and $AdjA$ denotes adjoint of matrix $A$) -

The number of arbitrary constants in the general solution of a differential equation of fourth order are:

If $f: A \rightarrow B$ given by $3^{f(x)}+2^{-x}=4$ is a bijection, then

The vectors $3\,i + j - 5\,k$ and $a\,i + b\,j - 15\,k$ are collinear, if

Choose the correct answer from the given four options:
The maximum value of $\sin\text{x}\cdot\cos\text{x}$ is: