An integral equation can determine a bound or coefficient: evaluate symbolically first, then solve the resulting equation. The accumulated value is determined by the endpoint antiderivative values, so a given integral value constrains those endpoints. Keep the unknown symbolic. Form upper minus lower, solve the algebraic, exponential, logarithmic or trigonometric equation, then apply the stated restrictions. _0b2x,dx=16, b>0 b2=16 b=4. Exam check: a square may produce two algebraic bounds; only those allowed by the question survive. Check that the chosen interval avoids all undefined points.

An integral equation can determine a bound or coefficient: evaluate symbolically first, then solve the resulting equation.

The accumulated value is determined by the endpoint antiderivative values, so a given integral value constrains those endpoints.

Keep the unknown symbolic. Form upper minus lower, solve the algebraic, exponential, logarithmic or trigonometric equation, then apply the stated restrictions.

\(\int_0^b2x\,\mathrm{d}x=16,\quad b>0\quad\Rightarrow\quad b^2=16\quad\Rightarrow\quad b=4\).

Exam check: a square may produce two algebraic bounds; only those allowed by the question survive. Check that the chosen interval avoids all undefined points.

Recovering limits and coefficients

Recovering limits and coefficients