Given that k k\,k is a positive constant and ∫1k(32x+9)dx=8\displaystyle \int_1^k \left( \frac{3}{2\sqrt{x}} + 9 \right) dx = 8∫1k(2x3+9)dx=8
Show that 9k+3k−20=09k + 3\sqrt{k} - 20 = 09k+3k−20=0
Hence, using algebra, find any values of k k\,k such that ∫1k(32x+9)dx=8\displaystyle \int_1^k \left( \frac{3}{2\sqrt{x}} + 9 \right) dx = 8∫1k(2x3+9)dx=8
51 exam-style questions on Edexcel AS Level Maths Integration, covering 13.1 Integrating x^n, 13.2 Indefinite Integrals, 13.3 Finding Functions, 13.4 Definite Integrals, 13.5 Areas under Curves, 13.6 Areas under the x-axis, and 13.7 Areas between curves and lines. Each one has a worked solution and a mark scheme showing where the marks go.