What's wrong with this solution of the $$ \int_0^1 15 \sqrt{9-5x} \, dx \enspace ?$$ $$= \enspace 15\int_0^1 \sqrt{9-5x} \, dx $$ $$ u=9-5x $$ $$ du = -5dx $$ $$ \frac{-15}{5} \int_0^1 \sqrt{u} \, du $$ $$ -3 \int_0^1 \sqrt{u} \, du $$ Which will later lead to the integral of $80$. Other answers say it is $38$. What technique did the use?
2026-04-03 10:46:34.1775213194
Definite integration technique
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The bounds on $u$ are wrong. $u=9-5x$ ranges from $9-5\cdot0$ to $9-5\cdot1$ since $x$ ranges from $0$ to $1$.