Additional Mathematics 0606 / Calculus — Integration / 3.853.85: Area between curve and line; integrals0606/21/M/J/23 — Question 7 · 10 marksMark as done · Save for later · Show all solutions(a)The diagram shows y=6x−x2y = 6x - x^{2}y=6x−x2 for 0⩽x⩽50 \leqslant x \leqslant 50⩽x⩽5 and the line y=xy = xy=x. Find the area of the shaded region.[4]▸ Answer(b)(i)Find ∫cos(2x3+1)⋅6x2 dx\displaystyle\int\mathrm{cos}\bigl(2x^{3} + 1\bigr)\cdot 6x^{2}\,\mathrm{d}x∫cos(2x3+1)⋅6x2dx.[3]▸ Answer(b)(ii)Find ∫4x1+2x2 dx\displaystyle\int\frac{4x}{1 + 2x^{2}}\,\mathrm{d}x∫1+2x24xdx.[3]▸ Answer▸ Official mark scheme← 3.56: Normal intersecting a cubic again; definite integral3.32: Differentiate ln of a cubic and integrate →
