MCQ
$\int\limits_0^{\pi /2} {\frac{{{{\sin }^3}\,x}}{{\sin \,x\, + \,\cos \,x}}} \,dx$ ની કિમંત મેળવો.
- A$\frac{{\pi \, - \,2}}{4}$
- B$\frac{{\pi \, - \,1}}{2}$
- ✓$\frac{{\pi \, - \,1}}{4}$
- D$\frac{{\pi \, - \,2}}{8}$
$\Rightarrow \mathrm{I}=\int_{0}^{\pi / 4} \frac{\sin ^{3} x+\cos ^{3} x}{\sin x+\cos x} d x$
$=\int_{0}^{\pi / 4}(1-\sin x \cos x) d x$
$=\left(x-\frac{\sin ^{2} x}{2}\right)_{0}^{\pi / 4}$
${=\frac{\pi}{4}-\frac{1}{4}}$
${=\frac{\pi-1}{4}}$
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