If _ 0 ^ 2 is equal to: 1. 1 2 2. 1 4 3. 2 4. 1 - Vidyadip

Question

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

$\frac{1}{2}$
$\frac{1}{4}$
$2$
$1$

✓

Answer

$\frac{1}{2}$

Solution:

$\int\limits_{0}^{\frac{\pi}{2}}\sin\text{x}\cos\text{xdx}$

$\sin\text{x}=\text{t}\Rightarrow\cos\text{xdx}=\text{dt}$

$\text{x}\Rightarrow0\Rightarrow\frac{\pi}{2}$

$\int\limits_{0}^{\frac{\pi}{2}}\text{tdt}$

$\Rightarrow\frac{\text{t}^2}{2}\mid^1_0$

$\Rightarrow\frac{1}{2}-0=\frac{1}{2}$

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

If $\text{A}=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 1 \\ \text{a} & \text{b} & 2 \end{bmatrix},$ then aI + bA + 2 A² equals:

A
-A
ab A
None of these.

If ${\cos ^{ - 1}}p + {\cos ^{ - 1}}q + {\cos ^{ - 1}}r = \pi $ then ${p^2} + {q^2} + {r^2} + 2pqr = $

Consider the function$f (x) = x\, cos x - sin x$, then identify the statement which is correct .

Let $h$ be a twice continuously differentiable positive function on an open interval $J.$ Let $g(x) = ln\left( {h(x)} \right)$ for each $x \in J$. Suppose ${\left( {h'(x)} \right)^2} > h''(x) h(x) $ for each $x \in J$. Then

If $f(x) = x, - 1 \le x \le 1$, then function $f(x)$ is

The general solution of differention eqution of the e^x dy + (ye^x + 2x)dx = 0 is:

xe^y + x²= C
xe^y+ y²= C
ye^x + y²= C
ye^y+ x² = C

Let the vectors $\vec{a}=(1+t) \hat{i}+(1-t) \hat{j}+\hat{k}$, $\overrightarrow{ b }=(1- t ) \hat{ i }+(1+ t ) \hat{ j }+2 \hat{ k }$ and $\overrightarrow{ c }=\hat{ i }- t \hat{ j }+\hat{ k }, t \in R$ be such that for $\alpha, \beta, \gamma \in R , \alpha \overrightarrow{ a }+\beta \overrightarrow{ b }+\gamma \overrightarrow{ c }=\overrightarrow{0}$ $\Rightarrow \alpha=\beta=\gamma=0$. Then, the set of all values of $t$ is.

If $f(x) = x^5 - 5x^4 + 5x^3 -10$ has local maximum and minimum at $x = p$ and $x = q$, respectively, then $(p, q)$ equals

If $y = 2x + {\cot ^{ - 1}}\,x + \log \left( {\sqrt {1 + {x^2}} - x} \right),$ then $y$

The radius of the base of a cone is increasing at the rate of 3cm/minute and the altitude is decreasing at the rate of 4cm/minute. The rate of change of lateral surface when the radius = 7cm and altitude 24cm is:

$54\pi \text{cm}^{2}/\text{min}$
$7\pi\text{cm}^{2}/\text{min}$
$27\text{cm}^{2}/\text{min}$
$\text{none of these }$