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

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

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