Integrating standard functionsEdexcel A-Level Maths: Mind map

Exam questions on Integrating standard functions

1. A curve has gradient $\frac{\mathrm{d}y}{\mathrm{d}x}=6e^{2x}-\frac{4}{x}$ for $x>0$, and passes through the point $(1,\,3e^2+1)$.
   Find the equation of the curve.2 marks
2. Angles are in radians. A function is defined by $f(x)=\sin3x+\cos\frac{x}{2}$.
   Find the exact value of $\int_0^{\pi}f(x)\,\mathrm{d}x$.2 marks
3. Angles are in radians. Trigonometric identities are used to rewrite an expression before it is integrated.
   Show that $\int\sin^2x\,\mathrm{d}x=\frac{x}{2}-\frac{\sin2x}{4}+c$.3 marks