INSTRUCTION

The assignment must be submitted by ${10}^{th}$ February $2025.$

$5\%$ mark will be deducted for any late submission.

$0\%$ mark will be given to any late submission more than TEN DAYS after the deadline.

QUESTIONS

For a function that is defined by $xsin3x,$

a$.$ Use integration by part to find ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xsin3xdx.$

b$.$ Using your answer to part $($a$),$ find ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{2}cos3xdx.$

$(10$ marks$)$

Given $f()=(2cos{)}^2-3si{n}^2.$

a$.$ Show that $f()=\frac{1}{2}\frac{7}{2}cos2.$

b$.$ Hence, find the exact value of ${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}f()d.$

$(10$ marks$)$

Given that

$\frac{x^3}{\sqrt[\phantom{2}]{x^{4}16}}$

a$.$ Use a suitable substitution to find

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3}{\sqrt[\phantom{2}]{x^{4}16}}dx$

b$.$ Hence, evaluate

${\displaystyle \underset{1}{\overset{4}{}}}\frac{x^3}{\sqrt[\phantom{2}]{x^{4}16}}dx$

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