Question

please bro help to solve pleaseplease bro help to solve please​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\int \limits^{ \frac{\pi}{2} } _{0} ( {cos}^{2} x) dx = 0.785}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt: \implies \int \limits^{ \frac{\pi}{2} } _{0} ( {cos}^{2} x) dx \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies \int \limits^{ \frac{\pi}{2} } _{0} ( {cos}^{2} x) dx =?$

• According to given question :

$\tt: \implies \int \limits^{ \frac{\pi}{2} } _{0} ( {cos}^{2} x) dx \\ \\ \tt\circ\:2\:cos^{2}=1+cos\:2x \\\\ \tt: \implies \int \limits^{ \frac{\pi}{2} } _{0} \bigg( \frac{1 + cos \: 2x}{2} \bigg )dx \\ \\ \tt: \implies \frac{1}{2} \int \limits^{ \frac{\pi}{2} } _{0} (1 + cos \: 2x)dx \\\\ \tt\circ\:\int cos\:x=sin\:x \\\\ \tt: \implies \frac{1}{2} \bigg[x + \frac{sin \: 2x}{2} \bigg]^{ \frac{\pi}{2} }_{0} \\ \\ \tt: \implies \frac{1}{2} \bigg[\bigg( \frac{\pi}{2} + \frac{sin \: 2 \times \frac{\pi}{2} }{2} \bigg) -\bigg( \frac{0}{2} + \frac{sin \: 2 \times 0}{2} \bigg)\bigg] \\ \\ \tt: \implies \frac{1}{2} \bigg[\bigg( \frac{3.14}{2} + \frac{sin \: \pi}{2}\bigg) - (0 + 0)\bigg] \\ \\ \tt: \implies \frac{1}{2} (1.57 + 0) \\ \\ \green{\tt: \implies 0.785} \\ \\ \green{\tt \therefore \int \limits^{ \frac{\pi}{2} } _{0} ( {cos}^{2} x) dx = 0.785}$

Answer 2

$\boxed{\underline{\rule{200}{10}}}$

✪ CHECK THE ATTACHMENT FOR THE SOLUTION ✪

$\boxed{\underline{\rule{200}{10}}}$