Question

AP Calculus BC Practice Question.

Please help me.

Answer 1

what on

Answer 2

u=5x du=5dx

Answer 3

\[\frac{1}{5}\int\limits \sin ^2(u) \cos ^2(u) \, du\]
\[\frac{1}{5}\int\limits \sin ^2(u) \left(1-\sin ^2(u)\right) \, du\]
factor
\[\frac{1}{5}\int\limits \left(\sin ^2(u)-\sin ^4(u)\right) \, du\]
split
\[\frac{1}{5}\int\limits \sin ^2(u) \, du-\frac{1}{5}\int\limits \sin ^4(u) \, du\]
half angle formula
\[\text{}=\frac{1}{5}\int\limits \left(\frac{1}{2}-\frac{1}{2} \cos (2 u)\right) \, du-\frac{1}{5}\int\limits \sin ^4(u) \, du\]

Answer 4

hmm

Answer 5

on simplification the question becomes(1/8)(1-cos20x) and on integrating gives (1/8)(x-(1/20)sin20x) +c

Answer 6

just use half angle formulas:\[\sin^2\theta=\frac{1-cos2\theta}{2}\]
\[\cos^2\theta=\frac{1+cos2\theta}{2}\] and simplify, integrate. You're good to go:)

Answer 7

Thank you @marco26 I forgot about the half angle formula^^.