JAMB - Mathematics (2001 - No. 25)
Evaluate \(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x\)
3/5(2x-3)5/3 + k
6/5(2x-3)5/3 + k
2x-3+k
2(2x-3)+k
Forklaring
\(\int 2(2x - 3)^{\frac{2}{3}} \mathrm d x\)
Let \(u = 2x - 3\)
\(\mathrm d u = 2 \mathrm d x\)
= \(\int u^{\frac{2}{3}} \mathrm d u\)
= \(\frac{u^{\frac{5}{3}}}{\frac{5}{3}} + k\)
= \(\frac{3}{5} (2x - 3)^{\frac{5}{3}} + k\)