Saved Bookmarks
| 1. |
Evaluate : ∫(1 − x)√x dx. |
|
Answer» ∫(1 − x)√x dx = ∫(√x − x√x) dx = ∫ (x \(\frac{1}{2}\) − x \(\frac{3}{2}\)) dx = ∫ x \(\frac{1}{2}\) − ∫ x \(\frac{3}{2}\) dx =\(\frac{2}{3} x ^{\frac{3}{2}}\) − \(\frac{2}{5} x^{\frac{5}{2}}\) + c, where C is an integral constant. (\(\because\) ∫ xndx = \(\big(\frac{x^{n+1}}{n+1}\big)\)) Hence, ∫(1-x)√x dx = \(\frac{2}{3} x ^{\frac{3}{2}}\) - \(\frac{2}{5} x^{\frac{5}{2}}\) + c. |
|