8.1 Assessed Exercises 1

Solutions in tutor’s pigeonhole by 17:00 on Tuesday 22nd November, please. Feedback is available from the moodle website.

A1.1. i) Factorize the polynomial $g(x)=x^{4}+2x^{3}+4x^{2}+8x$ as a product of linear factors and irreducible quadratic polynomials.

[1]

ii) Evaluate the definite integral

[6]

A1.2. Use the substitution $x=a\sinh u$ to work out the integral

You may assume the formulas

It may help to introduce $v$ such that $t=a\sinh v$.

[3]