Question

integrate (cosx-sinx)dx limit π/4 to 0​

Answer 1

Answer:

$\longrightarrow \: \displaystyle \sf\int\limits_{0}^{ \frac{\pi}{4} } \bigg( \cos(x) - \sin (x) \bigg) \,dx$

$\longrightarrow \: \displaystyle \sf \left. \sin(x) - \bigg( - \cos(x) \bigg)\right| _{0}^{ \frac{\pi}{4} }$

$\longrightarrow \: \displaystyle \sf \left. \bigg[\sin(x) + \cos(x) \bigg]\right| _{0}^{ \frac{\pi}{4} }$

$\longrightarrow \: \displaystyle \sf \bigg[\sin \bigg( \frac{\pi}{4} \bigg) -\sin (0) \bigg] + \bigg[\cos \bigg( \frac{\pi}{4} \bigg) - \cos(0) \bigg]$

$\longrightarrow \: \displaystyle \sf \bigg[\sin ( {45}^{ \circ} ) -\sin ( {0}^{ \circ} ) \bigg] + \bigg[\cos ( {45}^{ \circ} ) - \cos ( {0}^{ \circ} ) \bigg]$

$\longrightarrow \: \displaystyle \sf \bigg[ \frac{1}{ \sqrt{2} } -0 \bigg] + \bigg[ \frac{1}{ \sqrt{2} } - 1 \bigg]$

$\longrightarrow \: \displaystyle \sf \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } - 1$

$\longrightarrow \: \underline{ \boxed{ \displaystyle \orange{\bf \sqrt{2} - 1}}}$